10 33
From Knot Atlas
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(KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 33's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
Planar diagram presentation | X6271 X14,6,15,5 X20,15,1,16 X16,7,17,8 X8,19,9,20 X18,9,19,10 X10,17,11,18 X2,14,3,13 X12,4,13,3 X4,12,5,11 |
Gauss code | 1, -8, 9, -10, 2, -1, 4, -5, 6, -7, 10, -9, 8, -2, 3, -4, 7, -6, 5, -3 |
Dowker-Thistlethwaite code | 6 12 14 16 18 4 2 20 10 8 |
Conway Notation | [311113] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 12, width is 5, Braid index is 5 |
[{3, 9}, {2, 7}, {6, 8}, {7, 10}, {9, 5}, {4, 6}, {5, 11}, {10, 4}, {12, 3}, {11, 13}, {1, 12}, {13, 2}, {8, 1}] |
[edit Notes on presentations of 10 33]
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: {K11a333,}
Same Jones Polynomial (up to mirroring, ): {}
Vassiliev invariants
V2 and V3: | (0, 0) |
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 0 is the signature of 10 33. 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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