L10n37
From Knot Atlas
|
|
|
|
 (Knotscape image) | See the full Thistlethwaite Link Table (up to 11 crossings).
Visit L10n37's page at Knotilus. Visit L10n37's page at the original Knot Atlas. |
[edit] Link Presentations
[edit Notes on L10n37's Link Presentations]
| Planar diagram presentation | X6172 X12,3,13,4 X13,17,14,16 X9,15,10,14 X15,11,16,10 X17,5,18,20 X7,19,8,18 X19,9,20,8 X2536 X4,11,1,12 |
| Gauss code | {1, -9, 2, -10}, {9, -1, -7, 8, -4, 5, 10, -2, -3, 4, -5, 3, -6, 7, -8, 6} |
| A Braid Representative |
| ||||||
| A Morse Link Presentation | 
|
[edit] Polynomial invariants
| Multivariable Alexander Polynomial (in u, v, w, ...) | u5−vu4 + 2vu3−u3−vu2 + 2u2−u + v (db) |
| Jones polynomial |  (db)
|
| Signature | 1 (db) |
| HOMFLY-PT polynomial | −z5a−1 + z5a−3 + az3−7z3a−1 + 5z3a−3−z3a−5 + 4az−13za−1 + 9za−3−2za−5 + 4az−1−8a−1z−1 + 5a−3z−1−a−5z−1 (db) |
| Kauffman polynomial | −az7−z7a−1−z7a−3−z7a−5−2z6a−2−3z6a−4−2z6a−6−z6 + 7az5 + 9z5a−1 + 5z5a−3 + 2z5a−5−z5a−7 + 14z4a−2 + 13z4a−4 + 7z4a−6 + 8z4−15az3−23z3a−1−9z3a−3 + 2z3a−5 + 3z3a−7−28z2a−2−18z2a−4−5z2a−6−15z2 + 13az + 21za−1 + 8za−3−za−5−za−7 + 14a−2 + 9a−4 + 2a−6 + 8−4az−1−8a−1z−1−5a−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 = 1 is the signature of L10n37. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:L10n37/KhovanovTable |
| Integral Khovanov Homology
(db, data source) |
|
[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. |
|
