{{Rolfsen Knot Page| n = 10 | k = 25 | KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-2,6,-8,9,-7,10,-5,3,-4,2,-10,8,-9,7,-6,5/goTop.html | braid_table =
[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]
[[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[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:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]]
[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]]
| braid_crossings = 11 | braid_width = 4 | braid_index = 4 | same_alexander = [[10_56]], [[K11a140]], | same_jones = [[10_56]], | khovanov_table =
\ r
  \  
j \
 -8-7-6-5-4-3-2-1012χ
1          11
-1         1 -1
-3        41 3
-5       42  -2
-7      63   3
-9     54    -1
-11    56     -1
-13   45      1
-15  25       -3
-17 14        3
-19 2         -2
-211          1
| coloured_jones_2 = q^2-2 q+7 q^{-1} -9 q^{-2} -5 q^{-3} +26 q^{-4} -19 q^{-5} -23 q^{-6} +56 q^{-7} -24 q^{-8} -54 q^{-9} +85 q^{-10} -18 q^{-11} -82 q^{-12} +97 q^{-13} -4 q^{-14} -93 q^{-15} +86 q^{-16} +8 q^{-17} -78 q^{-18} +58 q^{-19} +11 q^{-20} -46 q^{-21} +26 q^{-22} +7 q^{-23} -17 q^{-24} +7 q^{-25} +2 q^{-26} -3 q^{-27} + q^{-28} | coloured_jones_3 = q^6-2 q^5+2 q^3+4 q^2-8 q-6+11 q^{-1} +20 q^{-2} -21 q^{-3} -34 q^{-4} +18 q^{-5} +71 q^{-6} -20 q^{-7} -101 q^{-8} -7 q^{-9} +153 q^{-10} +33 q^{-11} -186 q^{-12} -92 q^{-13} +230 q^{-14} +144 q^{-15} -243 q^{-16} -223 q^{-17} +261 q^{-18} +281 q^{-19} -246 q^{-20} -351 q^{-21} +232 q^{-22} +402 q^{-23} -203 q^{-24} -438 q^{-25} +165 q^{-26} +459 q^{-27} -128 q^{-28} -449 q^{-29} +79 q^{-30} +429 q^{-31} -48 q^{-32} -372 q^{-33} +8 q^{-34} +314 q^{-35} +9 q^{-36} -239 q^{-37} -25 q^{-38} +174 q^{-39} +27 q^{-40} -117 q^{-41} -21 q^{-42} +70 q^{-43} +17 q^{-44} -41 q^{-45} -10 q^{-46} +22 q^{-47} +5 q^{-48} -11 q^{-49} - q^{-50} +3 q^{-51} +2 q^{-52} -3 q^{-53} + q^{-54} | coloured_jones_4 = q^{12}-2 q^{11}+2 q^9-q^8+5 q^7-10 q^6-2 q^5+11 q^4+20 q^2-37 q-23+27 q^{-1} +20 q^{-2} +83 q^{-3} -83 q^{-4} -102 q^{-5} -3 q^{-6} +49 q^{-7} +272 q^{-8} -73 q^{-9} -237 q^{-10} -178 q^{-11} -26 q^{-12} +591 q^{-13} +123 q^{-14} -284 q^{-15} -505 q^{-16} -369 q^{-17} +877 q^{-18} +515 q^{-19} -57 q^{-20} -811 q^{-21} -986 q^{-22} +919 q^{-23} +929 q^{-24} +473 q^{-25} -898 q^{-26} -1697 q^{-27} +668 q^{-28} +1180 q^{-29} +1145 q^{-30} -727 q^{-31} -2296 q^{-32} +233 q^{-33} +1225 q^{-34} +1775 q^{-35} -402 q^{-36} -2677 q^{-37} -245 q^{-38} +1105 q^{-39} +2234 q^{-40} -16 q^{-41} -2775 q^{-42} -676 q^{-43} +831 q^{-44} +2427 q^{-45} +374 q^{-46} -2532 q^{-47} -948 q^{-48} +421 q^{-49} +2241 q^{-50} +677 q^{-51} -1951 q^{-52} -950 q^{-53} -9 q^{-54} +1697 q^{-55} +758 q^{-56} -1221 q^{-57} -682 q^{-58} -268 q^{-59} +1015 q^{-60} +593 q^{-61} -613 q^{-62} -331 q^{-63} -286 q^{-64} +476 q^{-65} +329 q^{-66} -262 q^{-67} -88 q^{-68} -178 q^{-69} +180 q^{-70} +134 q^{-71} -106 q^{-72} + q^{-73} -77 q^{-74} +60 q^{-75} +42 q^{-76} -42 q^{-77} +12 q^{-78} -24 q^{-79} +16 q^{-80} +11 q^{-81} -13 q^{-82} +5 q^{-83} -5 q^{-84} +3 q^{-85} +2 q^{-86} -3 q^{-87} + q^{-88} | coloured_jones_5 = | coloured_jones_6 = | coloured_jones_7 = | computer_talk = 
In[1]:=    
 
<< KnotTheory`
Loading KnotTheory` (version of August 29, 2005, 15:33:11)...
In[2]:= PD[Knot[10, 25]]
Out[2]:= PD[X[1, 4, 2, 5], X[5, 14, 6, 15], X[3, 13, 4, 12], X[13, 3, 14, 2], X[11, 20, 12, 1], X[19, 6, 20, 7], X[9, 18, 10, 19], X[7, 16, 8, 17], X[17, 8, 18, 9], X[15, 10, 16, 11]]
In[3]:= GaussCode[Knot[10, 25]]
Out[3]:= GaussCode[-1, 4, -3, 1, -2, 6, -8, 9, -7, 10, -5, 3, -4, 2, -10, 8, -9, 7, -6, 5]
In[4]:= DTCode[Knot[10, 25]]
Out[4]:= DTCode[4, 12, 14, 16, 18, 20, 2, 10, 8, 6]
In[5]:= br = BR[Knot[10, 25]]
Out[5]:= BR[4, {-1, -1, -1, -1, -2, 1, -2, -2, 3, -2, 3}]
In[6]:= {First[br], Crossings[br]}
Out[6]:= {4, 11}
In[7]:= BraidIndex[Knot[10, 25]]
Out[7]:= 4
In[8]:= Show[DrawMorseLink[Knot[10, 25]]]
[[Image:10_25_ML.gif]]
Out[8]:= -Graphics-
In[9]:= (#[Knot[10, 25]]&) /@ { SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex }
Out[9]:= {Reversible, 2, 3, 2, NotAvailable, 1}
In[10]:= alex = Alexander[Knot[10, 25]][t]
Out[10]:= 2 8 14 2 3 17 - -- + -- - -- - 14 t + 8 t - 2 t 3 2 t t t
In[11]:= Conway[Knot[10, 25]][z]
Out[11]:= 4 6 1 - 4 z - 2 z
In[12]:= Select[AllKnots[], (alex === Alexander[#][t])&]
Out[12]:= {Knot[10, 25], Knot[10, 56], Knot[11, Alternating, 140]}
In[13]:= {KnotDet[Knot[10, 25]], KnotSignature[Knot[10, 25]]}
Out[13]:= {65, -4}
In[14]:= Jones[Knot[10, 25]][q]
Out[14]:= -10 3 6 9 10 11 10 7 5 2 1 + q - -- + -- - -- + -- - -- + -- - -- + -- - - 9 8 7 6 5 4 3 2 q q q q q q q q q
In[15]:= Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]
Out[15]:= {Knot[10, 25], Knot[10, 56]}
In[16]:= A2Invariant[Knot[10, 25]][q]
Out[16]:= -30 -28 -26 -24 2 -20 3 -12 3 -8 1 + q - q + q + q - --- + q - --- - q + --- - q + 22 18 10 q q q 2 -4 -- + q 6 q
In[17]:= HOMFLYPT[Knot[10, 25]][a, z]
Out[17]:= 2 6 8 2 2 4 2 6 2 8 2 2 4 2 a - 2 a + a + 3 a z - 2 a z - 3 a z + 2 a z + a z - 4 4 6 4 8 4 4 6 6 6 3 a z - 3 a z + a z - a z - a z
In[18]:= Kauffman[Knot[10, 25]][a, z]
Out[18]:= 2 6 8 3 7 11 2 2 4 2 -2 a + 2 a + a + a z - 2 a z + a z + 5 a z + 4 a z - 6 2 8 2 10 2 12 2 3 3 5 3 7 3 4 a z + a z + 3 a z - a z + 4 a z + 2 a z + 3 a z + 9 3 11 3 2 4 4 4 6 4 8 4 2 a z - 3 a z - 4 a z - 3 a z + 3 a z - 5 a z - 10 4 12 4 3 5 5 5 7 5 9 5 6 a z + a z - 6 a z - 7 a z - 9 a z - 5 a z + 11 5 2 6 4 6 6 6 8 6 10 6 3 7 3 a z + a z - 3 a z - 8 a z + a z + 5 a z + 2 a z + 5 7 7 7 9 7 4 8 6 8 8 8 5 9 2 a z + 5 a z + 5 a z + 2 a z + 5 a z + 3 a z + a z + 7 9 a z
In[19]:= {Vassiliev[2][Knot[10, 25]], Vassiliev[3][Knot[10, 25]]}
Out[19]:= {0, 2}
In[20]:= Kh[Knot[10, 25]][q, t]
Out[20]:= 2 4 1 2 1 4 2 5 -- + -- + ------ + ------ + ------ + ------ + ------ + ------ + 5 3 21 8 19 7 17 7 17 6 15 6 15 5 q q q t q t q t q t q t q t 4 5 5 6 5 4 6 3 ------ + ------ + ------ + ------ + ----- + ----- + ----- + ---- + 13 5 13 4 11 4 11 3 9 3 9 2 7 2 7 q t q t q t q t q t q t q t q t 4 t t 2 ---- + -- + - + q t 5 3 q q t q
In[21]:= ColouredJones[Knot[10, 25], 2][q]
Out[21]:= -28 3 2 7 17 7 26 46 11 58 78 q - --- + --- + --- - --- + --- + --- - --- + --- + --- - --- + 27 26 25 24 23 22 21 20 19 18 q q q q q q q q q q 8 86 93 4 97 82 18 85 54 24 56 23 --- + --- - --- - --- + --- - --- - --- + --- - -- - -- + -- - -- - 17 16 15 14 13 12 11 10 9 8 7 6 q q q q q q q q q q q q 19 26 5 9 7 2 -- + -- - -- - -- + - - 2 q + q 5 4 3 2 q q q q q
}}