L11a11
From Knot Atlas
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![]() (Knotscape image) | See the full Thistlethwaite Link Table (up to 11 crossings).
Visit L11a11's page at Knotilus. Visit L11a11's page at the original Knot Atlas. |
[edit] Link Presentations
[edit Notes on L11a11's Link Presentations]
| Planar diagram presentation | X6172 X20,7,21,8 X4,21,1,22 X14,10,15,9 X8493 X12,5,13,6 X22,13,5,14 X18,16,19,15 X16,11,17,12 X10,17,11,18 X2,20,3,19 |
| Gauss code | {1, -11, 5, -3}, {6, -1, 2, -5, 4, -10, 9, -6, 7, -4, 8, -9, 10, -8, 11, -2, 3, -7} |
| A Braid Representative | | |||||
| A Morse Link Presentation |
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[edit] Polynomial invariants
| Multivariable Alexander Polynomial (in u, v, w, ...) | (db)
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| Jones polynomial | (db)
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| Signature | -1 (db) |
| HOMFLY-PT polynomial | a7(−z) + 3a5z3 + 3a5z−3a3z5−6a3z3−4a3z + az7 + 3az5−z5a−1 + 5az3−z3a−1 + 3az + az−1−za−1−a−1z−1 (db) |
| Kauffman polynomial | a8z6−2a8z4 + a8z2 + 4a7z7−9a7z5 + 7a7z3−2a7z + 7a6z8−14a6z6 + 10a6z4−3a6z2 + 6a5z9−22a5z5 + 23a5z3−6a5z + 2a4z10 + 20a4z8−53a4z6 + 41a4z4−10a4z2 + 15a3z9−9a3z7−34a3z5 + z5a−3 + 35a3z3−8a3z + 2a2z10 + 28a2z8−64a2z6 + 5z6a−2 + 41a2z4−3z4a−2−9a2z2 + 9az9 + 7az7 + 12z7a−1−38az5−16z5a−1 + 26az3 + 7z3a−1−6az−2za−1 + az−1 + a−1z−1 + 15z8−21z6 + 9z4−3z2−1 (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 L11a11. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:L11a11/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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