L11n218
From Knot Atlas
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 (Knotscape image) | See the full Thistlethwaite Link Table (up to 11 crossings).
Visit L11n218's page at Knotilus. Visit L11n218's page at the original Knot Atlas. |
[edit] Link Presentations
[edit Notes on L11n218's Link Presentations]
| Planar diagram presentation | X10,1,11,2 X8,9,1,10 X3,12,4,13 X22,16,9,15 X17,3,18,2 X21,4,22,5 X5,15,6,14 X13,21,14,20 X16,12,17,11 X19,7,20,6 X7,19,8,18 |
| Gauss code | {1, 5, -3, 6, -7, 10, -11, -2}, {2, -1, 9, 3, -8, 7, 4, -9, -5, 11, -10, 8, -6, -4} |
| 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, ...) | −vu3 + u3−vu2 + u2 + vu−u + v−1 (db) |
| Jones polynomial |  (db)
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| Signature | 0 (db) |
| HOMFLY-PT polynomial | −z5a−3−5z3a−3 + z3a−5 + az + 2za−1−6za−3 + 3za−5 + 2a−1z−1−3a−3z−1 + a−5z−1 (db) |
| Kauffman polynomial | −z9a−3−z9a−5−z8a−2−2z8a−4−z8a−6 + 7z7a−3 + 7z7a−5 + 7z6a−2 + 14z6a−4 + 7z6a−6−15z5a−3−15z5a−5−14z4a−2−28z4a−4−15z4a−6−z4−az3 + z3a−1 + 15z3a−3 + 13z3a−5 + 10z2a−2 + 18z2a−4 + 11z2a−6 + 3z2 + 2az−3za−1−11za−3−6za−5−3a−2−3a−4−a−6 + 2a−1z−1 + 3a−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 = 0 is the signature of L11n218. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:L11n218/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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