L11a1
From Knot Atlas
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![]() (Knotscape image) | See the full Thistlethwaite Link Table (up to 11 crossings).
Visit L11a1's page at Knotilus. Visit L11a1's page at the original Knot Atlas. |
[edit] Link Presentations
[edit Notes on L11a1's Link Presentations]
| Planar diagram presentation | X6172 X14,7,15,8 X4,15,1,16 X10,6,11,5 X8493 X20,12,21,11 X22,17,5,18 X18,21,19,22 X12,20,13,19 X16,10,17,9 X2,14,3,13 |
| Gauss code | {1, -11, 5, -3}, {4, -1, 2, -5, 10, -4, 6, -9, 11, -2, 3, -10, 7, -8, 9, -6, 8, -7} |
| A Braid Representative | | |||||
| A Morse Link Presentation |
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[edit] Polynomial invariants
| Multivariable Alexander Polynomial (in u, v, w, ...) | −vu5 + u5 + 6vu4−6u4−12vu3 + 12u3 + 12vu2−12u2−6vu + 6u + v−1 (db) |
| Jones polynomial | (db)
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| Signature | 1 (db) |
| HOMFLY-PT polynomial | −z7a−1 + 2az5−3z5a−1 + 2z5a−3−a3z3 + 3az3−4z3a−1 + 4z3a−3−z3a−5−az + 2za−3−za−5 + a3z−1−2az−1 + 2a−1z−1−a−3z−1 (db) |
| Kauffman polynomial | −2z10a−2−2z10−7az9−13z9a−1−6z9a−3−9a2z8−17z8a−2−9z8a−4−17z8−5a3z7 + 5az7 + 12z7a−1−6z7a−3−8z7a−5−a4z6 + 20a2z6 + 36z6a−2 + 9z6a−4−4z6a−6 + 44z6 + 10a3z5 + 14az5 + 16z5a−1 + 25z5a−3 + 12z5a−5−z5a−7 + a4z4−11a2z4−19z4a−2−z4a−4 + 5z4a−6−25z4−4a3z3−9az3−14z3a−1−18z3a−3−8z3a−5 + z3a−7 + 2z2a−2−z2a−4−2z2a−6 + z2−a3z−4az−2za−1 + 3za−3 + 2za−5 + 1 + a3z−1 + 2az−1 + 2a−1z−1 + a−3z−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 L11a1. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:L11a1/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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