10 50
From Knot Atlas
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See the full Rolfsen Knot Table. Visit 10 50's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
Planar diagram presentation | X6271 X8493 X2837 X16,10,17,9 X14,5,15,6 X4,15,5,16 X20,14,1,13 X10,20,11,19 X18,12,19,11 X12,18,13,17 |
Gauss code | 1, -3, 2, -6, 5, -1, 3, -2, 4, -8, 9, -10, 7, -5, 6, -4, 10, -9, 8, -7 |
Dowker-Thistlethwaite code | 6 8 14 2 16 18 20 4 12 10 |
Conway Notation | [32,3,2] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | ||||
Length is 11, width is 4, Braid index is 4 |
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![]() [{2, 12}, {1, 11}, {12, 10}, {11, 7}, {9, 4}, {10, 8}, {5, 3}, {4, 6}, {7, 5}, {6, 2}, {3, 9}, {8, 1}] |
[edit Notes on presentations of 10 50]
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: | (-1, -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 50. 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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