10 61
From Knot Atlas
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See the full Rolfsen Knot Table. Visit 10 61's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
10_61 is also known as the pretzel knot P(4,3,3). |
Knot presentations
Planar diagram presentation | X8291 X10,4,11,3 X2,10,3,9 X18,12,19,11 X14,7,15,8 X16,5,17,6 X6,15,7,16 X4,17,5,18 X20,14,1,13 X12,20,13,19 |
Gauss code | 1, -3, 2, -8, 6, -7, 5, -1, 3, -2, 4, -10, 9, -5, 7, -6, 8, -4, 10, -9 |
Dowker-Thistlethwaite code | 8 10 16 14 2 18 20 6 4 12 |
Conway Notation | [4,3,3] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | ||||
Length is 11, width is 4, Braid index is 4 |
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![]() [{6, 13}, {1, 12}, {13, 11}, {12, 4}, {10, 3}, {11, 9}, {8, 10}, {9, 7}, {5, 8}, {4, 2}, {3, 6}, {2, 5}, {7, 1}] |
[edit Notes on presentations of 10 61]
Three dimensional invariants
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Four dimensional invariants
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Polynomial invariants
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {}
Same Jones Polynomial (up to mirroring, ): {}
Vassiliev invariants
V2 and V3: | (-4, -5) |
V2,1 through V6,9: |
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V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.
Khovanov Homology
The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where 4 is the signature of 10 61. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
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Integral Khovanov Homology
(db, data source) |
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