From Knot Atlas
[edit] Link Presentations
[edit Notes on L9a14's Link Presentations]
| Planar diagram presentation
| X6172 X12,4,13,3 X14,8,15,7 X16,10,17,9 X18,12,5,11 X8,16,9,15 X10,18,11,17 X2536 X4,14,1,13
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| Gauss code
| {1, -8, 2, -9}, {8, -1, 3, -6, 4, -7, 5, -2, 9, -3, 6, -4, 7, -5}
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[edit] Polynomial invariants
| Multivariable Alexander Polynomial (in u, v, w, ...)
| −vu5 + u5 + vu4−u4−vu3 + u3 + vu2−u2−vu + u + v−1 (db)
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| Jones polynomial
|  (db)
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| Signature
| 5 (db)
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| HOMFLY-PT polynomial
| −z7a−5 + z5a−3−6z5a−5 + z5a−7 + 5z3a−3−12z3a−5 + 4z3a−7 + 7za−3−11za−5 + 4za−7 + 3a−3z−1−5a−5z−1 + 2a−7z−1 (db)
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| Kauffman polynomial
| −z8a−4−z8a−6−z7a−3−4z7a−5−3z7a−7 + 4z6a−4 + z6a−6−3z6a−8 + 6z5a−3 + 20z5a−5 + 11z5a−7−3z5a−9−z4a−4 + 8z4a−6 + 6z4a−8−3z4a−10−12z3a−3−30z3a−5−12z3a−7 + 4z3a−9−2z3a−11−8z2a−4−12z2a−6 + 3z2a−10−z2a−12 + 10za−3 + 17za−5 + 7za−7 + 5a−4 + 5a−6−a−10−3a−3z−1−5a−5z−1−2a−7z−1 (db)
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| 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 = 5 is the signature of L9a14. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.
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| Data:L9a14/KhovanovTable
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