View source for 10 59

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{{Rolfsen Knot Page|
n = 10 |
k = 59 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,3,-1,2,-10,5,-3,4,-2,6,-9,10,-5,7,-8,9,-6,8,-7/goTop.html |
braid_table     = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]]</td></tr>
</table> |
braid_crossings = 10 |
braid_width     = 5 |
braid_index     = 5 |
same_alexander  = [[9_40]], [[K11n66]],  |
same_jones      = [[10_106]],  |
khovanov_table  = <table border=1>
<tr align=center>
<td width=13.3333%><table cellpadding=0 cellspacing=0>
  <tr><td>\</td><td>&nbsp;</td><td>r</td></tr>
<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr>
<tr><td>j</td><td>&nbsp;</td><td>\</td></tr>
</table></td>
  <td width=6.66667%>-4</td    ><td width=6.66667%>-3</td    ><td width=6.66667%>-2</td    ><td width=6.66667%>-1</td    ><td width=6.66667%>0</td    ><td width=6.66667%>1</td    ><td width=6.66667%>2</td    ><td width=6.66667%>3</td    ><td width=6.66667%>4</td    ><td width=6.66667%>5</td    ><td width=6.66667%>6</td    ><td width=13.3333%>&chi;</td></tr>
<tr align=center><td>15</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td>1</td></tr>
<tr align=center><td>13</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>11</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>3</td></tr>
<tr align=center><td>9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>-4</td></tr>
<tr align=center><td>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr>
<tr align=center><td>-1</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-3</td></tr>
<tr align=center><td>-3</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr>
<tr align=center><td>-5</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>-7</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
</table> |
coloured_jones_2 = <math>q^{20}-3 q^{19}+2 q^{18}+6 q^{17}-17 q^{16}+12 q^{15}+22 q^{14}-53 q^{13}+26 q^{12}+56 q^{11}-100 q^{10}+29 q^9+95 q^8-127 q^7+16 q^6+117 q^5-119 q^4-7 q^3+112 q^2-83 q-25+81 q^{-1} -39 q^{-2} -27 q^{-3} +40 q^{-4} -9 q^{-5} -14 q^{-6} +11 q^{-7} -3 q^{-9} + q^{-10} </math> |
coloured_jones_3 = <math>q^{39}-3 q^{38}+2 q^{37}+2 q^{36}-q^{35}-8 q^{34}+9 q^{33}+14 q^{32}-23 q^{31}-27 q^{30}+48 q^{29}+53 q^{28}-85 q^{27}-101 q^{26}+132 q^{25}+175 q^{24}-183 q^{23}-267 q^{22}+211 q^{21}+391 q^{20}-232 q^{19}-504 q^{18}+217 q^{17}+610 q^{16}-178 q^{15}-691 q^{14}+122 q^{13}+730 q^{12}-42 q^{11}-748 q^{10}-27 q^9+711 q^8+118 q^7-665 q^6-182 q^5+573 q^4+255 q^3-481 q^2-286 q+358+307 q^{-1} -245 q^{-2} -291 q^{-3} +138 q^{-4} +251 q^{-5} -56 q^{-6} -191 q^{-7} - q^{-8} +133 q^{-9} +24 q^{-10} -77 q^{-11} -30 q^{-12} +39 q^{-13} +23 q^{-14} -16 q^{-15} -14 q^{-16} +6 q^{-17} +5 q^{-18} -3 q^{-20} + q^{-21} </math> |
coloured_jones_4 = <math>q^{64}-3 q^{63}+2 q^{62}+2 q^{61}-5 q^{60}+8 q^{59}-11 q^{58}+11 q^{57}+4 q^{56}-33 q^{55}+29 q^{54}-13 q^{53}+53 q^{52}-2 q^{51}-150 q^{50}+47 q^{49}+44 q^{48}+229 q^{47}-q^{46}-494 q^{45}-71 q^{44}+180 q^{43}+757 q^{42}+186 q^{41}-1157 q^{40}-612 q^{39}+204 q^{38}+1758 q^{37}+886 q^{36}-1891 q^{35}-1692 q^{34}-274 q^{33}+2903 q^{32}+2192 q^{31}-2188 q^{30}-2929 q^{29}-1351 q^{28}+3594 q^{27}+3638 q^{26}-1811 q^{25}-3696 q^{24}-2626 q^{23}+3524 q^{22}+4612 q^{21}-991 q^{20}-3719 q^{19}-3609 q^{18}+2852 q^{17}+4866 q^{16}-56 q^{15}-3125 q^{14}-4127 q^{13}+1833 q^{12}+4499 q^{11}+836 q^{10}-2120 q^9-4177 q^8+630 q^7+3613 q^6+1555 q^5-855 q^4-3700 q^3-508 q^2+2306 q+1817+367 q^{-1} -2651 q^{-2} -1163 q^{-3} +887 q^{-4} +1437 q^{-5} +1091 q^{-6} -1343 q^{-7} -1095 q^{-8} -105 q^{-9} +677 q^{-10} +1074 q^{-11} -347 q^{-12} -575 q^{-13} -397 q^{-14} +77 q^{-15} +618 q^{-16} +50 q^{-17} -129 q^{-18} -250 q^{-19} -115 q^{-20} +215 q^{-21} +66 q^{-22} +26 q^{-23} -75 q^{-24} -75 q^{-25} +45 q^{-26} +15 q^{-27} +23 q^{-28} -9 q^{-29} -21 q^{-30} +6 q^{-31} +5 q^{-33} -3 q^{-35} + q^{-36} </math> |
coloured_jones_5 = <math>q^{95}-3 q^{94}+2 q^{93}+2 q^{92}-5 q^{91}+4 q^{90}+5 q^{89}-9 q^{88}+q^{87}+4 q^{86}-17 q^{85}+11 q^{84}+32 q^{83}-4 q^{82}-22 q^{81}-41 q^{80}-49 q^{79}+50 q^{78}+155 q^{77}+101 q^{76}-115 q^{75}-315 q^{74}-273 q^{73}+163 q^{72}+669 q^{71}+638 q^{70}-185 q^{69}-1235 q^{68}-1341 q^{67}+41 q^{66}+2021 q^{65}+2581 q^{64}+489 q^{63}-2989 q^{62}-4499 q^{61}-1653 q^{60}+3912 q^{59}+7115 q^{58}+3765 q^{57}-4486 q^{56}-10276 q^{55}-6985 q^{54}+4288 q^{53}+13723 q^{52}+11201 q^{51}-3061 q^{50}-16799 q^{49}-16208 q^{48}+544 q^{47}+19255 q^{46}+21420 q^{45}+2918 q^{44}-20420 q^{43}-26301 q^{42}-7214 q^{41}+20423 q^{40}+30315 q^{39}+11642 q^{38}-19211 q^{37}-33076 q^{36}-15851 q^{35}+17079 q^{34}+34581 q^{33}+19447 q^{32}-14466 q^{31}-34836 q^{30}-22171 q^{29}+11463 q^{28}+34118 q^{27}+24228 q^{26}-8535 q^{25}-32600 q^{24}-25448 q^{23}+5395 q^{22}+30482 q^{21}+26291 q^{20}-2395 q^{19}-27787 q^{18}-26495 q^{17}-905 q^{16}+24567 q^{15}+26408 q^{14}+4043 q^{13}-20727 q^{12}-25537 q^{11}-7347 q^{10}+16367 q^9+24111 q^8+10123 q^7-11590 q^6-21606 q^5-12422 q^4+6642 q^3+18415 q^2+13587 q-2015-14338 q^{-1} -13643 q^{-2} -1920 q^{-3} +10000 q^{-4} +12425 q^{-5} +4685 q^{-6} -5718 q^{-7} -10237 q^{-8} -6122 q^{-9} +2092 q^{-10} +7441 q^{-11} +6285 q^{-12} +556 q^{-13} -4635 q^{-14} -5428 q^{-15} -2035 q^{-16} +2191 q^{-17} +4023 q^{-18} +2550 q^{-19} -507 q^{-20} -2531 q^{-21} -2278 q^{-22} -464 q^{-23} +1262 q^{-24} +1700 q^{-25} +798 q^{-26} -431 q^{-27} -1037 q^{-28} -752 q^{-29} -12 q^{-30} +520 q^{-31} +535 q^{-32} +178 q^{-33} -201 q^{-34} -325 q^{-35} -164 q^{-36} +49 q^{-37} +141 q^{-38} +122 q^{-39} +19 q^{-40} -71 q^{-41} -64 q^{-42} -9 q^{-43} +12 q^{-44} +24 q^{-45} +23 q^{-46} -9 q^{-47} -14 q^{-48} - q^{-49} +5 q^{-52} -3 q^{-54} + q^{-55} </math> |
coloured_jones_6 = <math>q^{132}-3 q^{131}+2 q^{130}+2 q^{129}-5 q^{128}+4 q^{127}+q^{126}+7 q^{125}-19 q^{124}+q^{123}+20 q^{122}-25 q^{121}+16 q^{120}+18 q^{119}+21 q^{118}-73 q^{117}-31 q^{116}+64 q^{115}-44 q^{114}+82 q^{113}+112 q^{112}+42 q^{111}-292 q^{110}-247 q^{109}+90 q^{108}+21 q^{107}+497 q^{106}+606 q^{105}+152 q^{104}-1059 q^{103}-1376 q^{102}-425 q^{101}+220 q^{100}+2204 q^{99}+2916 q^{98}+1258 q^{97}-2865 q^{96}-5443 q^{95}-3951 q^{94}-726 q^{93}+6525 q^{92}+10723 q^{91}+7429 q^{90}-4175 q^{89}-15120 q^{88}-16463 q^{87}-8829 q^{86}+11686 q^{85}+28398 q^{84}+27511 q^{83}+3240 q^{82}-28283 q^{81}-44153 q^{80}-35885 q^{79}+6963 q^{78}+53013 q^{77}+69038 q^{76}+33878 q^{75}-31299 q^{74}-82485 q^{73}-89733 q^{72}-24463 q^{71}+67566 q^{70}+124650 q^{69}+94827 q^{68}-5378 q^{67}-110736 q^{66}-159124 q^{65}-88087 q^{64}+51617 q^{63}+169514 q^{62}+170878 q^{61}+53259 q^{60}-107320 q^{59}-215770 q^{58}-165370 q^{57}+2969 q^{56}+181264 q^{55}+232043 q^{54}+124295 q^{53}-71352 q^{52}-237847 q^{51}-226639 q^{50}-57865 q^{49}+159895 q^{48}+258830 q^{47}+180526 q^{46}-22299 q^{45}-226671 q^{44}-255929 q^{43}-107466 q^{42}+122916 q^{41}+254329 q^{40}+210290 q^{39}+20838 q^{38}-197919 q^{37}-258084 q^{36}-138340 q^{35}+85001 q^{34}+232503 q^{33}+219810 q^{32}+54199 q^{31}-162683 q^{30}-245235 q^{29}-157373 q^{28}+47338 q^{27}+201336 q^{26}+218957 q^{25}+84517 q^{24}-120303 q^{23}-222151 q^{22}-171612 q^{21}+4097 q^{20}+158404 q^{19}+208727 q^{18}+115433 q^{17}-65976 q^{16}-183941 q^{15}-177651 q^{14}-44691 q^{13}+99222 q^{12}+180816 q^{11}+138738 q^{10}-2953 q^9-125398 q^8-163229 q^7-86074 q^6+29317 q^5+128622 q^4+138288 q^3+51737 q^2-53665 q-120386-100518 q^{-1} -31211 q^{-2} +60715 q^{-3} +105510 q^{-4} +76269 q^{-5} +8646 q^{-6} -59455 q^{-7} -79642 q^{-8} -59587 q^{-9} +1761 q^{-10} +53025 q^{-11} +63614 q^{-12} +38668 q^{-13} -6747 q^{-14} -38361 q^{-15} -51131 q^{-16} -26219 q^{-17} +8138 q^{-18} +31017 q^{-19} +34299 q^{-20} +17373 q^{-21} -3803 q^{-22} -24902 q^{-23} -23742 q^{-24} -11308 q^{-25} +4420 q^{-26} +15214 q^{-27} +15812 q^{-28} +9456 q^{-29} -4507 q^{-30} -9950 q^{-31} -10160 q^{-32} -5012 q^{-33} +1515 q^{-34} +6152 q^{-35} +7515 q^{-36} +2307 q^{-37} -919 q^{-38} -3667 q^{-39} -3731 q^{-40} -2189 q^{-41} +469 q^{-42} +2720 q^{-43} +1729 q^{-44} +1151 q^{-45} -279 q^{-46} -1025 q^{-47} -1360 q^{-48} -625 q^{-49} +458 q^{-50} +384 q^{-51} +612 q^{-52} +269 q^{-53} -387 q^{-55} -305 q^{-56} +13 q^{-57} -27 q^{-58} +134 q^{-59} +108 q^{-60} +88 q^{-61} -67 q^{-62} -71 q^{-63} +2 q^{-64} -33 q^{-65} +12 q^{-66} +15 q^{-67} +32 q^{-68} -9 q^{-69} -14 q^{-70} +6 q^{-71} -7 q^{-72} +5 q^{-75} -3 q^{-77} + q^{-78} </math> |
coloured_jones_7 = <math>q^{175}-3 q^{174}+2 q^{173}+2 q^{172}-5 q^{171}+4 q^{170}+q^{169}+3 q^{168}-3 q^{167}-19 q^{166}+17 q^{165}+12 q^{164}-20 q^{163}+12 q^{162}+3 q^{161}+13 q^{160}-18 q^{159}-78 q^{158}+56 q^{157}+67 q^{156}-14 q^{155}+39 q^{154}-35 q^{153}-21 q^{152}-111 q^{151}-247 q^{150}+152 q^{149}+325 q^{148}+266 q^{147}+262 q^{146}-232 q^{145}-506 q^{144}-785 q^{143}-920 q^{142}+363 q^{141}+1475 q^{140}+2037 q^{139}+1839 q^{138}-467 q^{137}-2745 q^{136}-4522 q^{135}-4567 q^{134}-245 q^{133}+5220 q^{132}+9665 q^{131}+10101 q^{130}+2561 q^{129}-8323 q^{128}-18334 q^{127}-21216 q^{126}-9528 q^{125}+10914 q^{124}+32221 q^{123}+41491 q^{122}+25211 q^{121}-10127 q^{120}-51064 q^{119}-74442 q^{118}-56212 q^{117}-608 q^{116}+72262 q^{115}+123499 q^{114}+110369 q^{113}+30341 q^{112}-89468 q^{111}-187950 q^{110}-194369 q^{109}-91202 q^{108}+90580 q^{107}+262071 q^{106}+312183 q^{105}+195053 q^{104}-60419 q^{103}-333639 q^{102}-459859 q^{101}-349449 q^{100}-17771 q^{99}+383829 q^{98}+625054 q^{97}+554478 q^{96}+156798 q^{95}-391708 q^{94}-787693 q^{93}-798981 q^{92}-360028 q^{91}+339456 q^{90}+921759 q^{89}+1060754 q^{88}+620370 q^{87}-216558 q^{86}-1004231 q^{85}-1313097 q^{84}-916642 q^{83}+27372 q^{82}+1017968 q^{81}+1525433 q^{80}+1221199 q^{79}+214803 q^{78}-959249 q^{77}-1677609 q^{76}-1503543 q^{75}-482798 q^{74}+836629 q^{73}+1756491 q^{72}+1737910 q^{71}+750054 q^{70}-668316 q^{69}-1765174 q^{68}-1909362 q^{67}-990367 q^{66}+478970 q^{65}+1715130 q^{64}+2013147 q^{63}+1186804 q^{62}-290062 q^{61}-1624327 q^{60}-2057064 q^{59}-1333116 q^{58}+119079 q^{57}+1512667 q^{56}+2053620 q^{55}+1430994 q^{54}+26504 q^{53}-1393841 q^{52}-2018872 q^{51}-1491657 q^{50}-146548 q^{49}+1278259 q^{48}+1966185 q^{47}+1525924 q^{46}+247682 q^{45}-1165838 q^{44}-1904384 q^{43}-1547603 q^{42}-339934 q^{41}+1054432 q^{40}+1836659 q^{39}+1563270 q^{38}+433405 q^{37}-934402 q^{36}-1760650 q^{35}-1578328 q^{34}-535662 q^{33}+799050 q^{32}+1669468 q^{31}+1588648 q^{30}+650127 q^{29}-638978 q^{28}-1554650 q^{27}-1589201 q^{26}-773601 q^{25}+452900 q^{24}+1406920 q^{23}+1566532 q^{22}+898023 q^{21}-240689 q^{20}-1220620 q^{19}-1510509 q^{18}-1009004 q^{17}+13846 q^{16}+994613 q^{15}+1407490 q^{14}+1089286 q^{13}+214501 q^{12}-735297 q^{11}-1253458 q^{10}-1122016 q^9-421402 q^8+458102 q^7+1047594 q^6+1093289 q^5+586349 q^4-183526 q^3-802844 q^2-999366 q-688534-61652 q^{-1} +538408 q^{-2} +844839 q^{-3} +717559 q^{-4} +254425 q^{-5} -281280 q^{-6} -648043 q^{-7} -673235 q^{-8} -376793 q^{-9} +58547 q^{-10} +434006 q^{-11} +568182 q^{-12} +423484 q^{-13} +108117 q^{-14} -231142 q^{-15} -425527 q^{-16} -402092 q^{-17} -207529 q^{-18} +64525 q^{-19} +272883 q^{-20} +330682 q^{-21} +241488 q^{-22} +51003 q^{-23} -135388 q^{-24} -234540 q^{-25} -223883 q^{-26} -111853 q^{-27} +31530 q^{-28} +137589 q^{-29} +174030 q^{-30} +126180 q^{-31} +32687 q^{-32} -57695 q^{-33} -113998 q^{-34} -109320 q^{-35} -59734 q^{-36} +4273 q^{-37} +59446 q^{-38} +77364 q^{-39} +60427 q^{-40} +23421 q^{-41} -19957 q^{-42} -44848 q^{-43} -46742 q^{-44} -30772 q^{-45} -2624 q^{-46} +19304 q^{-47} +29060 q^{-48} +26577 q^{-49} +11643 q^{-50} -3586 q^{-51} -14239 q^{-52} -18098 q^{-53} -12038 q^{-54} -3445 q^{-55} +4502 q^{-56} +9813 q^{-57} +8779 q^{-58} +5232 q^{-59} +428 q^{-60} -4316 q^{-61} -5140 q^{-62} -4126 q^{-63} -1847 q^{-64} +1118 q^{-65} +2202 q^{-66} +2606 q^{-67} +1934 q^{-68} +94 q^{-69} -822 q^{-70} -1286 q^{-71} -1165 q^{-72} -354 q^{-73} -12 q^{-74} +464 q^{-75} +739 q^{-76} +340 q^{-77} +92 q^{-78} -184 q^{-79} -290 q^{-80} -119 q^{-81} -142 q^{-82} -34 q^{-83} +142 q^{-84} +103 q^{-85} +74 q^{-86} -9 q^{-87} -56 q^{-88} +6 q^{-89} -33 q^{-90} -33 q^{-91} +12 q^{-92} +15 q^{-93} +23 q^{-94} -14 q^{-96} +6 q^{-97} -7 q^{-99} +5 q^{-102} -3 q^{-104} + q^{-105} </math> |
computer_talk = 
         <table>
         <tr valign=top>
         <td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td>
         <td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td>
         </tr>
         <tr valign=top><td colspan=2>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Knot[10, 59]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[4, 2, 5, 1], X[10, 6, 11, 5], X[8, 3, 9, 4], X[2, 9, 3, 10], 
 
  X[14, 8, 15, 7], X[18, 12, 19, 11], X[20, 15, 1, 16], 
 
  X[16, 19, 17, 20], X[12, 18, 13, 17], X[6, 14, 7, 13]]</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[3]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>GaussCode[Knot[10, 59]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[1, -4, 3, -1, 2, -10, 5, -3, 4, -2, 6, -9, 10, -5, 7, -8, 9, 
 
  -6, 8, -7]</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[4]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>DTCode[Knot[10, 59]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>DTCode[4, 8, 10, 14, 2, 18, 6, 20, 12, 16]</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[5]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>br = BR[Knot[10, 59]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[5, {-1, 2, -1, 2, -3, 2, 2, 4, -3, 4}]</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[6]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{First[br], Crossings[br]}</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{5, 10}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>BraidIndex[Knot[10, 59]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>5</nowiki></pre></td></tr>
         <tr  valign=top><td><pre style="color: blue; border: 0px; padding:  0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red;  border: 0px; padding:  0em"><nowiki>Show[DrawMorseLink[Knot[10, 59]]]</nowiki></pre></td></tr><tr><td></td><td  align=left>[[Image:10_59_ML.gif]]</td></tr><tr valign=top><td><tt><font  color=blue>Out[8]=</font></tt><td><tt><font  color=black>-Graphics-</font></tt></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>(#[Knot[10, 59]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Reversible, 1, 3, 3, NotAvailable, 1}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Knot[10, 59]][t]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>       -3   7    18             2    3
-23 + t   - -- + -- + 18 t - 7 t  + t
             2   t
            t</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[11]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[Knot[10, 59]][z]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>     2    4    6
1 - z  - z  + z</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[12]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[9, 40], Knot[10, 59], Knot[11, NonAlternating, 66]}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{KnotDet[Knot[10, 59]], KnotSignature[Knot[10, 59]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{75, 2}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[14]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Jones[Knot[10, 59]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>      -3   3    6              2       3       4      5      6    7
-9 + q   - -- + - + 12 q - 12 q  + 12 q  - 10 q  + 6 q  - 3 q  + q
            2   q
           q</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[15]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 59], Knot[10, 106]}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[16]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>A2Invariant[Knot[10, 59]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[16]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -10    -6   2    2       2    4      6    8    10    12      14
q    - q   + -- - -- + 2 q  - q  + 4 q  - q  + q   - q   - 3 q   + 
              4    2
             q    q
 
     16    18    22
  2 q   - q   + q</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[17]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>HOMFLYPT[Knot[10, 59]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[17]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>                                  2      2      2
      -6   3    4     2      2   z    4 z    5 z     2  2      4
-2 + a   - -- + -- + a  - 4 z  + -- - ---- + ---- + a  z  - 2 z  - 
            4    2                6     4      2
           a    a                a     a      a
 
     4      4    6
  2 z    3 z    z
  ---- + ---- + --
    4      2     2
   a      a     a</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[18]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Knot[10, 59]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[18]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>                                                           2      2
      -6   3    4     2   z    4 z   5 z              2   z    3 z
-2 - a   - -- - -- - a  + -- - --- - --- - 2 a z + 8 z  - -- + ---- + 
            4    2         7    3     a                    8     6
           a    a         a    a                          a     a
 
      2       2                3      3       3       3
  10 z    11 z       2  2   3 z    4 z    20 z    21 z         3
  ----- + ----- + 3 a  z  - ---- + ---- + ----- + ----- + 8 a z  - 
    4       2                 7      5      3       a
   a       a                 a      a      a
 
          4      4       4      4                5      5       5
     4   z    5 z    11 z    8 z       2  4   3 z    7 z    28 z
  6 z  + -- - ---- - ----- - ---- - 3 a  z  + ---- - ---- - ----- - 
          8     6      4       2                7      5      3
         a     a      a       a                a      a      a
 
      5                      6    6      6              7       7
  27 z         5      6   5 z    z    9 z     2  6   6 z    11 z
  ----- - 9 a z  - 4 z  + ---- + -- - ---- + a  z  + ---- + ----- + 
    a                       6     4     2              5      3
                           a     a     a              a      a
 
     7                      8      8    9    9
  8 z         7      8   4 z    7 z    z    z
  ---- + 3 a z  + 3 z  + ---- + ---- + -- + --
   a                       4      2     3   a
                          a      a     a</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[19]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{Vassiliev[2][Knot[10, 59]], Vassiliev[3][Knot[10, 59]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[19]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{-1, -1}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[20]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Knot[10, 59]][q, t]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[20]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>         3     1       2       1       4      2      5    4 q
7 q + 6 q  + ----- + ----- + ----- + ----- + ---- + --- + --- + 
              7  4    5  3    3  3    3  2      2   q t    t
             q  t    q  t    q  t    q  t    q t
 
     3        5        5  2      7  2      7  3      9  3      9  4
  6 q  t + 6 q  t + 6 q  t  + 6 q  t  + 4 q  t  + 6 q  t  + 2 q  t  + 
 
     11  4    11  5      13  5    15  6
  4 q   t  + q   t  + 2 q   t  + q   t</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[21]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>ColouredJones[Knot[10, 59], 2][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[21]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>       -10   3    11   14   9    40   27   39   81               2
-25 + q    - -- + -- - -- - -- + -- - -- - -- + -- - 83 q + 112 q  - 
              9    7    6    5    4    3    2   q
             q    q    q    q    q    q    q
 
     3        4        5       6        7       8       9        10
  7 q  - 119 q  + 117 q  + 16 q  - 127 q  + 95 q  + 29 q  - 100 q   + 
 
      11       12       13       14       15       16      17      18
  56 q   + 26 q   - 53 q   + 22 q   + 12 q   - 17 q   + 6 q   + 2 q   - 
 
     19    20
  3 q   + q</nowiki></pre></td></tr>
         </table>  }}