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{{Knot Navigation Links|ext=gif}}

{{Rolfsen Knot Page Header|n=9|k=34|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,3,-7,6,-1,2,-3,5,-6,8,-9,7,-5,4,-2,9,-8/goTop.html}}

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{{:{{PAGENAME}} Further Notes and Views}}

{{Knot Presentations}}

<center><table border=1 cellpadding=10><tr align=center valign=top>
<td>
[[Braid Representatives|Minimum Braid Representative]]:
<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:BraidPart3.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:BraidPart4.gif]][[Image:BraidPart1.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:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr>
</table>

[[Invariants from Braid Theory|Length]] is 9, width is 4.

[[Invariants from Braid Theory|Braid index]] is 4.
</td>
<td>
[[Lightly Documented Features|A Morse Link Presentation]]:

[[Image:{{PAGENAME}}_ML.gif]]
</td>
</tr></table></center>

{{3D Invariants}}
{{4D Invariants}}
{{Polynomial Invariants}}

=== "Similar" Knots (within the Atlas) ===

Same [[The Alexander-Conway Polynomial|Alexander/Conway Polynomial]]:
{[[K11n32]], [[K11n119]], ...}

Same [[The Jones Polynomial|Jones Polynomial]] (up to mirroring, <math>q\leftrightarrow q^{-1}</math>): 
{...}

{{Vassiliev Invariants}}

{{Khovanov Homology|table=<table border=1>
<tr align=center>
<td width=14.2857%><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=7.14286%>-5</td  ><td width=7.14286%>-4</td  ><td width=7.14286%>-3</td  ><td width=7.14286%>-2</td  ><td width=7.14286%>-1</td  ><td width=7.14286%>0</td  ><td width=7.14286%>1</td  ><td width=7.14286%>2</td  ><td width=7.14286%>3</td  ><td width=7.14286%>4</td  ><td width=14.2857%>&chi;</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>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td>1</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>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>&nbsp;</td><td>-3</td></tr>
<tr align=center><td>5</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>5</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>4</td></tr>
<tr align=center><td>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>7</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>-1</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 bgcolor=yellow>4</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</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 bgcolor=yellow>3</td><td bgcolor=yellow>6</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>-7</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>-3</td></tr>
<tr align=center><td>-9</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>3</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>-11</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>-1</td></tr>
</table>}}

{{Display Coloured Jones|J2=<math>q^{12}-4 q^{11}+4 q^{10}+10 q^9-29 q^8+12 q^7+47 q^6-74 q^5+6 q^4+101 q^3-109 q^2-17 q+140-112 q^{-1} -41 q^{-2} +143 q^{-3} -83 q^{-4} -54 q^{-5} +109 q^{-6} -39 q^{-7} -48 q^{-8} +55 q^{-9} -6 q^{-10} -24 q^{-11} +14 q^{-12} +2 q^{-13} -4 q^{-14} + q^{-15} </math>|J3=<math>q^{24}-4 q^{23}+4 q^{22}+6 q^{21}-9 q^{20}-19 q^{19}+20 q^{18}+56 q^{17}-42 q^{16}-116 q^{15}+49 q^{14}+214 q^{13}-26 q^{12}-350 q^{11}-25 q^{10}+482 q^9+132 q^8-611 q^7-258 q^6+693 q^5+410 q^4-747 q^3-536 q^2+741 q+652-707 q^{-1} -728 q^{-2} +632 q^{-3} +778 q^{-4} -532 q^{-5} -793 q^{-6} +410 q^{-7} +771 q^{-8} -269 q^{-9} -714 q^{-10} +126 q^{-11} +623 q^{-12} -7 q^{-13} -492 q^{-14} -87 q^{-15} +354 q^{-16} +129 q^{-17} -218 q^{-18} -130 q^{-19} +113 q^{-20} +97 q^{-21} -40 q^{-22} -63 q^{-23} +12 q^{-24} +27 q^{-25} -9 q^{-27} -2 q^{-28} +4 q^{-29} - q^{-30} </math>|J4=<math>q^{40}-4 q^{39}+4 q^{38}+6 q^{37}-13 q^{36}+q^{35}-11 q^{34}+39 q^{33}+37 q^{32}-90 q^{31}-49 q^{30}-48 q^{29}+221 q^{28}+257 q^{27}-272 q^{26}-385 q^{25}-384 q^{24}+633 q^{23}+1098 q^{22}-183 q^{21}-1115 q^{20}-1643 q^{19}+743 q^{18}+2693 q^{17}+949 q^{16}-1582 q^{15}-3886 q^{14}-277 q^{13}+4168 q^{12}+3112 q^{11}-926 q^{10}-6066 q^9-2301 q^8+4550 q^7+5225 q^6+689 q^5-7160 q^4-4285 q^3+3852 q^2+6391 q+2405-7085 q^{-1} -5517 q^{-2} +2637 q^{-3} +6547 q^{-4} +3731 q^{-5} -6164 q^{-6} -5993 q^{-7} +1158 q^{-8} +5920 q^{-9} +4680 q^{-10} -4533 q^{-11} -5807 q^{-12} -524 q^{-13} +4516 q^{-14} +5119 q^{-15} -2308 q^{-16} -4761 q^{-17} -2001 q^{-18} +2412 q^{-19} +4597 q^{-20} -136 q^{-21} -2852 q^{-22} -2485 q^{-23} +330 q^{-24} +3002 q^{-25} +993 q^{-26} -861 q^{-27} -1744 q^{-28} -721 q^{-29} +1195 q^{-30} +844 q^{-31} +189 q^{-32} -641 q^{-33} -622 q^{-34} +191 q^{-35} +277 q^{-36} +256 q^{-37} -76 q^{-38} -211 q^{-39} -15 q^{-40} +17 q^{-41} +74 q^{-42} +12 q^{-43} -33 q^{-44} -3 q^{-45} -5 q^{-46} +9 q^{-47} +2 q^{-48} -4 q^{-49} + q^{-50} </math>|J5=<math>q^{60}-4 q^{59}+4 q^{58}+6 q^{57}-13 q^{56}-3 q^{55}+9 q^{54}+8 q^{53}+20 q^{52}-q^{51}-74 q^{50}-72 q^{49}+59 q^{48}+181 q^{47}+190 q^{46}-60 q^{45}-449 q^{44}-571 q^{43}-30 q^{42}+957 q^{41}+1364 q^{40}+462 q^{39}-1505 q^{38}-2883 q^{37}-1772 q^{36}+1892 q^{35}+5191 q^{34}+4347 q^{33}-1364 q^{32}-7900 q^{31}-8689 q^{30}-897 q^{29}+10381 q^{28}+14640 q^{27}+5444 q^{26}-11494 q^{25}-21368 q^{24}-12686 q^{23}+10324 q^{22}+27973 q^{21}+21796 q^{20}-6404 q^{19}-32886 q^{18}-31910 q^{17}-198 q^{16}+35624 q^{15}+41435 q^{14}+8486 q^{13}-35518 q^{12}-49461 q^{11}-17413 q^{10}+33241 q^9+55091 q^8+25783 q^7-29202 q^6-58452 q^5-32910 q^4+24528 q^3+59579 q^2+38437 q-19500-59226 q^{-1} -42519 q^{-2} +14722 q^{-3} +57635 q^{-4} +45366 q^{-5} -9932 q^{-6} -55165 q^{-7} -47442 q^{-8} +5096 q^{-9} +51828 q^{-10} +48808 q^{-11} +119 q^{-12} -47403 q^{-13} -49515 q^{-14} -5832 q^{-15} +41709 q^{-16} +49272 q^{-17} +11825 q^{-18} -34528 q^{-19} -47595 q^{-20} -17694 q^{-21} +25954 q^{-22} +44084 q^{-23} +22696 q^{-24} -16564 q^{-25} -38434 q^{-26} -25897 q^{-27} +7098 q^{-28} +30858 q^{-29} +26727 q^{-30} +1204 q^{-31} -22142 q^{-32} -24730 q^{-33} -7381 q^{-34} +13309 q^{-35} +20490 q^{-36} +10678 q^{-37} -5684 q^{-38} -14834 q^{-39} -11161 q^{-40} +191 q^{-41} +9102 q^{-42} +9415 q^{-43} +2841 q^{-44} -4309 q^{-45} -6681 q^{-46} -3662 q^{-47} +1183 q^{-48} +3834 q^{-49} +3097 q^{-50} +451 q^{-51} -1768 q^{-52} -2043 q^{-53} -810 q^{-54} +531 q^{-55} +1028 q^{-56} +678 q^{-57} -7 q^{-58} -438 q^{-59} -373 q^{-60} -86 q^{-61} +126 q^{-62} +147 q^{-63} +79 q^{-64} -22 q^{-65} -67 q^{-66} -23 q^{-67} +9 q^{-68} +9 q^{-69} +8 q^{-70} +5 q^{-71} -9 q^{-72} -2 q^{-73} +4 q^{-74} - q^{-75} </math>|J6=<math>q^{84}-4 q^{83}+4 q^{82}+6 q^{81}-13 q^{80}-3 q^{79}+5 q^{78}+28 q^{77}-11 q^{76}-18 q^{75}+15 q^{74}-87 q^{73}-16 q^{72}+93 q^{71}+214 q^{70}+60 q^{69}-172 q^{68}-226 q^{67}-596 q^{66}-201 q^{65}+616 q^{64}+1477 q^{63}+1095 q^{62}-260 q^{61}-1676 q^{60}-3767 q^{59}-2705 q^{58}+1083 q^{57}+6329 q^{56}+7879 q^{55}+4218 q^{54}-3277 q^{53}-14376 q^{52}-16750 q^{51}-7389 q^{50}+12518 q^{49}+28184 q^{48}+29057 q^{47}+10529 q^{46}-27268 q^{45}-53389 q^{44}-48973 q^{43}-4566 q^{42}+51710 q^{41}+87565 q^{40}+72590 q^{39}-6610 q^{38}-94578 q^{37}-136646 q^{36}-85215 q^{35}+30912 q^{34}+151409 q^{33}+191466 q^{32}+92051 q^{31}-82084 q^{30}-229420 q^{29}-229647 q^{28}-78266 q^{27}+154170 q^{26}+312752 q^{25}+257079 q^{24}+23502 q^{23}-255646 q^{22}-371665 q^{21}-251033 q^{20}+63988 q^{19}+363413 q^{18}+413536 q^{17}+186123 q^{16}-191750 q^{15}-441171 q^{14}-408894 q^{13}-75882 q^{12}+328123 q^{11}+497760 q^{10}+330085 q^9-83203 q^8-430541 q^7-498059 q^6-197997 q^5+250860 q^4+508808 q^3+414062 q^2+14014 q-380135-523707 q^{-1} -273997 q^{-2} +175604 q^{-3} +482484 q^{-4} +448797 q^{-5} +83170 q^{-6} -323134 q^{-7} -517342 q^{-8} -318813 q^{-9} +109774 q^{-10} +442844 q^{-11} +462028 q^{-12} +141818 q^{-13} -259898 q^{-14} -495577 q^{-15} -356319 q^{-16} +34442 q^{-17} +384479 q^{-18} +463670 q^{-19} +209578 q^{-20} -170599 q^{-21} -447370 q^{-22} -389077 q^{-23} -65372 q^{-24} +286036 q^{-25} +435588 q^{-26} +280278 q^{-27} -44606 q^{-28} -348258 q^{-29} -389585 q^{-30} -173593 q^{-31} +140530 q^{-32} +348024 q^{-33} +315023 q^{-34} +92020 q^{-35} -193995 q^{-36} -321541 q^{-37} -239573 q^{-38} -16250 q^{-39} +199049 q^{-40} +271427 q^{-41} +178557 q^{-42} -29574 q^{-43} -186479 q^{-44} -217687 q^{-45} -115811 q^{-46} +42172 q^{-47} +156660 q^{-48} +170542 q^{-49} +71966 q^{-50} -45861 q^{-51} -123612 q^{-52} -118831 q^{-53} -48992 q^{-54} +38852 q^{-55} +94087 q^{-56} +80016 q^{-57} +30049 q^{-58} -29789 q^{-59} -61282 q^{-60} -55241 q^{-61} -18946 q^{-62} +22114 q^{-63} +38216 q^{-64} +33982 q^{-65} +11198 q^{-66} -11458 q^{-67} -24328 q^{-68} -20110 q^{-69} -5535 q^{-70} +5890 q^{-71} +13020 q^{-72} +10756 q^{-73} +4175 q^{-74} -3742 q^{-75} -6640 q^{-76} -4888 q^{-77} -2203 q^{-78} +1492 q^{-79} +2913 q^{-80} +2695 q^{-81} +623 q^{-82} -680 q^{-83} -1006 q^{-84} -1063 q^{-85} -320 q^{-86} +212 q^{-87} +552 q^{-88} +242 q^{-89} +59 q^{-90} -27 q^{-91} -163 q^{-92} -92 q^{-93} -26 q^{-94} +72 q^{-95} +16 q^{-96} +2 q^{-97} +15 q^{-98} -14 q^{-99} -8 q^{-100} -5 q^{-101} +9 q^{-102} +2 q^{-103} -4 q^{-104} + q^{-105} </math>|J7=<math>q^{112}-4 q^{111}+4 q^{110}+6 q^{109}-13 q^{108}-3 q^{107}+5 q^{106}+24 q^{105}+9 q^{104}-49 q^{103}-2 q^{102}+2 q^{101}-31 q^{100}+28 q^{99}+75 q^{98}+158 q^{97}+48 q^{96}-291 q^{95}-318 q^{94}-260 q^{93}-66 q^{92}+534 q^{91}+917 q^{90}+1208 q^{89}+482 q^{88}-1471 q^{87}-2844 q^{86}-3329 q^{85}-1711 q^{84}+2371 q^{83}+6470 q^{82}+9138 q^{81}+6836 q^{80}-2254 q^{79}-13194 q^{78}-21631 q^{77}-19779 q^{76}-3481 q^{75}+20489 q^{74}+43605 q^{73}+49176 q^{72}+25233 q^{71}-21814 q^{70}-75414 q^{69}-103193 q^{68}-77368 q^{67}+217 q^{66}+106234 q^{65}+185323 q^{64}+179387 q^{63}+71464 q^{62}-113375 q^{61}-286642 q^{60}-341928 q^{59}-223202 q^{58}+56051 q^{57}+375169 q^{56}+559280 q^{55}+480840 q^{54}+112560 q^{53}-400811 q^{52}-797484 q^{51}-843686 q^{50}-430400 q^{49}+298839 q^{48}+993820 q^{47}+1278907 q^{46}+910274 q^{45}-15765 q^{44}-1073367 q^{43}-1718343 q^{42}-1520174 q^{41}-470669 q^{40}+964613 q^{39}+2073346 q^{38}+2192067 q^{37}+1139954 q^{36}-633602 q^{35}-2263880 q^{34}-2829249 q^{33}-1922465 q^{32}+89307 q^{31}+2235800 q^{30}+3341119 q^{29}+2725638 q^{28}+609765 q^{27}-1986923 q^{26}-3661296 q^{25}-3449927 q^{24}-1377286 q^{23}+1555703 q^{22}+3768099 q^{21}+4023424 q^{20}+2119469 q^{19}-1015128 q^{18}-3681754 q^{17}-4408420 q^{16}-2762212 q^{15}+444233 q^{14}+3454987 q^{13}+4609291 q^{12}+3261430 q^{11}+87493 q^{10}-3149968 q^9-4658362 q^8-3610169 q^7-537899 q^6+2826220 q^5+4604709 q^4+3825894 q^3+890834 q^2-2522244 q-4494135-3945409 q^{-1} -1157376 q^{-2} +2257688 q^{-3} +4364984 q^{-4} +4006145 q^{-5} +1360966 q^{-6} -2029292 q^{-7} -4235883 q^{-8} -4042274 q^{-9} -1535296 q^{-10} +1820136 q^{-11} +4112104 q^{-12} +4076227 q^{-13} +1709872 q^{-14} -1604177 q^{-15} -3981713 q^{-16} -4116003 q^{-17} -1909743 q^{-18} +1351280 q^{-19} +3823412 q^{-20} +4156866 q^{-21} +2147420 q^{-22} -1036621 q^{-23} -3607912 q^{-24} -4177817 q^{-25} -2420560 q^{-26} +641548 q^{-27} +3304202 q^{-28} +4148097 q^{-29} +2710187 q^{-30} -164342 q^{-31} -2887912 q^{-32} -4027779 q^{-33} -2978499 q^{-34} -377124 q^{-35} +2346613 q^{-36} +3778094 q^{-37} +3175544 q^{-38} +942327 q^{-39} -1691930 q^{-40} -3373205 q^{-41} -3244729 q^{-42} -1469069 q^{-43} +962632 q^{-44} +2808633 q^{-45} +3139347 q^{-46} +1886766 q^{-47} -224497 q^{-48} -2115194 q^{-49} -2838187 q^{-50} -2127516 q^{-51} -438709 q^{-52} +1355500 q^{-53} +2354958 q^{-54} +2150543 q^{-55} +946552 q^{-56} -617661 q^{-57} -1746377 q^{-58} -1954553 q^{-59} -1238823 q^{-60} -6866 q^{-61} +1097392 q^{-62} +1583164 q^{-63} +1299853 q^{-64} +447271 q^{-65} -504567 q^{-66} -1116612 q^{-67} -1160225 q^{-68} -672613 q^{-69} +46196 q^{-70} +648950 q^{-71} +889664 q^{-72} +700205 q^{-73} +237065 q^{-74} -260227 q^{-75} -574945 q^{-76} -587886 q^{-77} -349646 q^{-78} -1773 q^{-79} +292569 q^{-80} +407982 q^{-81} +333928 q^{-82} +133949 q^{-83} -89221 q^{-84} -229710 q^{-85} -249493 q^{-86} -162516 q^{-87} -23369 q^{-88} +93644 q^{-89} +149147 q^{-90} +132781 q^{-91} +63605 q^{-92} -14057 q^{-93} -69180 q^{-94} -83861 q^{-95} -59274 q^{-96} -18707 q^{-97} +19848 q^{-98} +41277 q^{-99} +39464 q^{-100} +23395 q^{-101} +1684 q^{-102} -15056 q^{-103} -19946 q^{-104} -16215 q^{-105} -7040 q^{-106} +2517 q^{-107} +7576 q^{-108} +8655 q^{-109} +5620 q^{-110} +985 q^{-111} -1979 q^{-112} -3381 q^{-113} -2854 q^{-114} -1311 q^{-115} -33 q^{-116} +1072 q^{-117} +1289 q^{-118} +675 q^{-119} +178 q^{-120} -253 q^{-121} -344 q^{-122} -232 q^{-123} -197 q^{-124} +20 q^{-125} +141 q^{-126} +92 q^{-127} +39 q^{-128} -24 q^{-129} -21 q^{-130} +5 q^{-131} -26 q^{-132} -10 q^{-133} +14 q^{-134} +8 q^{-135} +5 q^{-136} -9 q^{-137} -2 q^{-138} +4 q^{-139} - q^{-140} </math>}}

{{Computer Talk Header}}

<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><pre style="border: 0px; padding: 0em">Loading KnotTheory` (version of August 29, 2005, 15:27:48)...</pre></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[9, 34]]</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[6, 2, 7, 1], X[16, 8, 17, 7], X[8, 3, 9, 4], X[2, 15, 3, 16], 
 
  X[14, 9, 15, 10], X[10, 6, 11, 5], X[4, 14, 5, 13], X[18, 11, 1, 12], 
 
  X[12, 17, 13, 18]]</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[9, 34]]</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, -7, 6, -1, 2, -3, 5, -6, 8, -9, 7, -5, 4, -2, 9, -8]</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[9, 34]]</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[6, 8, 10, 16, 14, 18, 4, 2, 12]</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[9, 34]]</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[4, {-1, 2, -1, 2, -3, 2, -1, 2, -3}]</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>{4, 9}</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[9, 34]]</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>4</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[9, 34]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_34_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[9, 34]]&) /@ {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, {4, 6}, 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[9, 34]][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   6    16             2    3
23 - t   + -- - -- - 16 t + 6 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[9, 34]][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    6
1 - 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, 34], Knot[11, NonAlternating, 32], 
 
  Knot[11, NonAlternating, 119]}</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[9, 34]], KnotSignature[Knot[9, 34]]}</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>{69, 0}</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[9, 34]][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>      -5   4    7    10   12             2      3    4
12 - q   + -- - -- + -- - -- - 10 q + 8 q  - 4 q  + q
            4    3    2   q
           q    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[9, 34]}</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[9, 34]][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>      -16    -14    2     2    2     -6    -4   2       2      4    6
-2 - q    + q    + --- - --- + -- - q   - q   + -- + 3 q  - 2 q  + q  + 
                    12    10    8                2
                   q     q     q                q
 
     8      10    12
  2 q  - 2 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[9, 34]][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                             4
      -2    2      2   z       2  2    4  2      4   z       2  4    6
-1 + a   + a  - 4 z  + -- + 3 a  z  - a  z  - 3 z  + -- + 2 a  z  - z
                        2                             2
                       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[9, 34]][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                           3
      -2    2   z             2   4 z        2  2      4  2   2 z
-1 - a   - a  - - - a z + 11 z  + ---- + 10 a  z  + 3 a  z  - ---- + 
                a                   2                           3
                                   a                           a
 
     3                                        4       4
  4 z          3      3  3    5  3       4   z    10 z        2  4
  ---- + 12 a z  + 5 a  z  - a  z  - 23 z  + -- - ----- - 19 a  z  - 
   a                                          4     2
                                             a     a
 
               5       5                                          6
     4  4   4 z    10 z          5       3  5    5  5      6   8 z
  7 a  z  + ---- - ----- - 26 a z  - 11 a  z  + a  z  + 9 z  + ---- + 
              3      a                                           2
             a                                                  a
 
                         7
     2  6      4  6   8 z          7      3  7      8      2  8
  5 a  z  + 4 a  z  + ---- + 14 a z  + 6 a  z  + 3 z  + 3 a  z
                       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[9, 34]], Vassiliev[3][Knot[9, 34]]}</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, 0}</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[9, 34]][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>6           1        3       1       4       3       6       4
- + 7 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + 
q          11  5    9  4    7  4    7  3    5  3    5  2    3  2
          q   t    q  t    q  t    q  t    q  t    q  t    q  t
 
   6      6               3        3  2      5  2    5  3      7  3
  ---- + --- + 5 q t + 5 q  t + 3 q  t  + 5 q  t  + q  t  + 3 q  t  + 
   3     q t
  q  t
 
   9  4
  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[9, 34], 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>       -15    4     2    14    24     6    55   48   39   109   54
140 + q    - --- + --- + --- - --- - --- + -- - -- - -- + --- - -- - 
              14    13    12    11    10    9    8    7    6     5
             q     q     q     q     q     q    q    q    q     q
 
  83   143   41   112               2        3      4       5       6
  -- + --- - -- - --- - 17 q - 109 q  + 101 q  + 6 q  - 74 q  + 47 q  + 
   4    3     2    q
  q    q     q
 
      7       8       9      10      11    12
  12 q  - 29 q  + 10 q  + 4 q   - 4 q   + q</nowiki></pre></td></tr>

</table>

See/edit the [[Rolfsen_Splice_Template]].

 [[Category:Knot Page]]