L10n9
From Knot Atlas
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 (Knotscape image) | See the full Thistlethwaite Link Table (up to 11 crossings).
Visit L10n9's page at Knotilus. Visit L10n9's page at the original Knot Atlas. |
[edit] Link Presentations
[edit Notes on L10n9's Link Presentations]
| Planar diagram presentation | X6172 X16,7,17,8 X4,17,1,18 X9,14,10,15 X8493 X5,11,6,10 X11,5,12,20 X13,19,14,18 X19,13,20,12 X2,16,3,15 |
| Gauss code | {1, -10, 5, -3}, {-6, -1, 2, -5, -4, 6, -7, 9, -8, 4, 10, -2, 3, 8, -9, 7} |
| A Braid Representative |
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| A Morse Link Presentation | 
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[edit] Polynomial invariants
| Multivariable Alexander Polynomial (in u, v, w, ...) | −vu + u + v−1 (db) |
| Jones polynomial |  (db)
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| Signature | -1 (db) |
| HOMFLY-PT polynomial | a3z−1−za−az−1−za−1−a−1z−1 + z3a−3 + 3za−3 + 2a−3z−1−za−5−a−5z−1 (db) |
| Kauffman polynomial | −z8a−2−z8a−4−z7a−1−2z7a−3−z7a−5 + 6z6a−2 + 6z6a−4 + 6z5a−1 + 12z5a−3 + 6z5a−5−11z4a−2−10z4a−4−z4−11z3a−1−21z3a−3−10z3a−5 + 9z2a−2 + 5z2a−4 + 4z2−a3z−az + 8za−1 + 13za−3 + 5za−5−a2−3a−2−a−4−2 + a3z−1 + az−1−a−1z−1−2a−3z−1−a−5z−1 (db) |
[edit] Khovanov Homology
| The coefficients of the monomials trqj are shown, along with their alternating sums χ (fixed j, alternation over r). The squares with yellow highlighting are those on the "critical diagonals", where j−2r = s + 1 or j−2r = s−1, where s = -1 is the signature of L10n9. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:L10n9/KhovanovTable |
| Integral Khovanov Homology
(db, data source) |
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[edit] Computer Talk
Much of the above data can be recomputed by Mathematica using the packageKnotTheory`. See A Sample KnotTheory` Session.[edit] Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Link Page master template (intermediate). See/edit the Link_Splice_Base (expert). Back to the top. |
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