L8n7
From Knot Atlas
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 (Knotscape image) | See the full Thistlethwaite Link Table (up to 11 crossings).
Visit L8n7's page at Knotilus. Visit L8n7's page at the original Knot Atlas. |
[edit] Link Presentations
[edit Notes on L8n7's Link Presentations]
| Planar diagram presentation | X6172 X2536 X11,13,12,16 X3,11,4,10 X9,1,10,4 X7,15,8,14 X13,5,14,8 X15,9,16,12 |
| Gauss code | {1, -2, -4, 5}, {2, -1, -6, 7}, {-5, 4, -3, 8}, {-7, 6, -8, 3} |
| 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, ...) | −uv + uwv−wv + uxv + w−ux−wx + x (db) |
| Jones polynomial |  (db)
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| Signature | 1 (db) |
| HOMFLY-PT polynomial | −2z3a−3 + 3za−1−6za−3 + 3za−5 + 3a−1z−1−7a−3z−1 + 5a−5z−1−a−7z−1 + a−1z−3−3a−3z−3 + 3a−5z−3−a−7z−3 (db) |
| Kauffman polynomial | −z6a−4−z6a−6−4z5a−3−5z5a−5−z5a−7−3z4a−2−2z4a−4 + z4a−6 + 12z3a−3 + 16z3a−5 + 4z3a−7 + 6z2a−2 + 12z2a−4 + 6z2a−6−6za−1−14za−3−14za−5−6za−7−8a−2−15a−4−8a−6 + 4a−1z−1 + 9a−3z−1 + 9a−5z−1 + 4a−7z−1 + 3a−2z−2 + 6a−4z−2 + 3a−6z−2−a−1z−3−3a−3z−3−3a−5z−3−a−7z−3 (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 L8n7. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:L8n7/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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