10 54
From Knot Atlas
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See the full Rolfsen Knot Table. Visit 10 54's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
Planar diagram presentation | X1425 X3,10,4,11 X7,12,8,13 X11,8,12,9 X13,19,14,18 X5,17,6,16 X17,7,18,6 X15,1,16,20 X19,15,20,14 X9,2,10,3 |
Gauss code | -1, 10, -2, 1, -6, 7, -3, 4, -10, 2, -4, 3, -5, 9, -8, 6, -7, 5, -9, 8 |
Dowker-Thistlethwaite code | 4 10 16 12 2 8 18 20 6 14 |
Conway Notation | [23,3,2] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | ||||
Length is 11, width is 4, Braid index is 4 |
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![]() [{12, 4}, {3, 10}, {9, 11}, {10, 12}, {11, 8}, {6, 9}, {5, 7}, {4, 6}, {2, 5}, {1, 3}, {8, 2}, {7, 1}] |
[edit Notes on presentations of 10 54]
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: {10_12,}
Same Jones Polynomial (up to mirroring, ): {}
Vassiliev invariants
V2 and V3: | (4, 2) |
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 2 is the signature of 10 54. 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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