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Input data and context
% 7_4-1
s.r1.x0.x0.x0.x0.x1.x1.u2
,1
% Symmetry 1 of a 2-bridge knot corresponding to the fraction 15/-4 = [-4,4] (Sakuma, Prop. 3.6, symmetry 1).
% Simplifies with options '-qs' to l2.l3.x2.x4.x4.x2.x1.x2.x1.x2.x1.x2.x1.x1.x2.x1.x1.x1.x2.x1.x2.x1.x1.x2.y3.y4.y4.y3.y2.u1.x1.x2.x1.y0.y1.u2.x0
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxBNr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 0 q^ 1 δ^1/2 ⬮——D—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯
2) h^11 q^18 δ^ -2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 7 q^12 δ^ -1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^ 3 q^ 6 δ^ 0 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxBNr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 0 q^ 1 δ^1/2 ⬮——D—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯
2) h^11 q^18 δ^ -2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 7 q^12 δ^ -1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^ 3 q^ 6 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxBNr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 0 q^ 1 δ^1/2 ⬮——D—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯
2) h^11 q^18 δ^ -2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 7 q^12 δ^ -1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^ 3 q^ 6 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxBNr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 0 q^ 1 δ^1/2 ⬮——D—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯
2) h^11 q^18 δ^ -2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 7 q^12 δ^ -1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^ 3 q^ 6 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxBNr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 0 q^ 1 δ^1/2 ⬮——D—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯
2) h^11 q^18 δ^ -2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 7 q^12 δ^ -1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^ 3 q^ 6 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxKhr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-1 q^ 0 δ^ 1 ⬮~~S^2~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯<~⬮<—⬮<~⬮<— r(-1/4) q^24/5 δ|^1
2) h^10 q^17 δ^-3/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^-2
3) h^11 q^19 δ^-3/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^24 δ|^-2
4) h^ 6 q^11 δ^-1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^-1
5) h^ 7 q^13 δ^-1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^-1
6) h^ 2 q^ 5 δ^ 1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^10 δ|^0
7) h^ 3 q^ 7 δ^ 1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^12 δ|^0
8) h^-1 q^ 1 δ^ 3/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^6 δ|^1
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxKhr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-1 q^ 0 δ^ 1 ⬮~~(-S^2)~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯<~⬮<—⬮<~⬮<— r(-1/4) q^24/5 δ|^1
2) h^10 q^17 δ^-3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^-2
3) h^11 q^19 δ^-3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^24 δ|^-2
4) h^ 6 q^11 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^-1
5) h^ 7 q^13 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^-1
6) h^ 2 q^ 5 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^10 δ|^0
7) h^ 3 q^ 7 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^12 δ|^0
8) h^-1 q^ 1 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^6 δ|^1
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxKhr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-1 q^ 0 δ^ 1 ⬮~~(-S^2)~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯<~⬮<—⬮<~⬮<— r(-1/4) q^24/5 δ|^1
2) h^10 q^17 δ^-3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^-2
3) h^11 q^19 δ^-3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^24 δ|^-2
4) h^ 6 q^11 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^-1
5) h^ 7 q^13 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^-1
6) h^ 2 q^ 5 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^10 δ|^0
7) h^ 3 q^ 7 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^12 δ|^0
8) h^-1 q^ 1 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^6 δ|^1
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxKhr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-1 q^ 0 δ^ 1 ⬮~~(-S^2)~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯<~⬮<—⬮<~⬮<— r(-1/4) q^24/5 δ|^1
2) h^10 q^17 δ^-3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^-2
3) h^11 q^19 δ^-3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^24 δ|^-2
4) h^ 6 q^11 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^-1
5) h^ 7 q^13 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^-1
6) h^ 2 q^ 5 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^10 δ|^0
7) h^ 3 q^ 7 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^12 δ|^0
8) h^-1 q^ 1 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^6 δ|^1
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxKhr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-1 q^ 0 δ^ 1 ⬮~~(-S^2)~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯<~⬮<—⬮<~⬮<— r(-1/4) q^24/5 δ|^1
2) h^10 q^17 δ^-3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^-2
3) h^11 q^19 δ^-3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^24 δ|^-2
4) h^ 6 q^11 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^-1
5) h^ 7 q^13 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^-1
6) h^ 2 q^ 5 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^10 δ|^0
7) h^ 3 q^ 7 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^12 δ|^0
8) h^-1 q^ 1 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^6 δ|^1
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c0
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxCKh-c0', generated by kht, version v0.1, on Sun Mar 7 15:45:53 2021 GMT
1) h^0 q^ 2 δ^1 ⬮
2) h^1 q^ 4 δ^1 ⬮——H—>⬮
3) h^1 q^ 4 δ^1 ⬮——H—>⬮
4) h^2 q^ 6 δ^1 ⬮——H—>⬮
5) h^3 q^ 8 δ^1 ⬮——H—>⬮
6) h^4 q^10 δ^1 ⬮——H—>⬮
7) h^4 q^10 δ^1 ⬮——H—>⬮
8) h^6 q^14 δ^1 ⬮——H—>⬮
options -c2
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxCKh-c2', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^0 q^ 2 δ^1 ⬮
2) h^1 q^ 4 δ^1 ⬮——H—>⬮
3) h^1 q^ 4 δ^1 ⬮——H—>⬮
4) h^2 q^ 6 δ^1 ⬮——H—>⬮
5) h^3 q^ 8 δ^1 ⬮——H—>⬮
6) h^4 q^10 δ^1 ⬮——H—>⬮
7) h^4 q^10 δ^1 ⬮——H—>⬮
8) h^6 q^14 δ^1 ⬮——H—>⬮
options -c3
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxCKh-c3', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^0 q^ 2 δ^1 ⬮
2) h^1 q^ 4 δ^1 ⬮——H—>⬮
3) h^1 q^ 4 δ^1 ⬮——H—>⬮
4) h^2 q^ 6 δ^1 ⬮——H—>⬮
5) h^3 q^ 8 δ^1 ⬮——H—>⬮
6) h^4 q^10 δ^1 ⬮——H—>⬮
7) h^4 q^10 δ^1 ⬮——H—>⬮
8) h^6 q^14 δ^1 ⬮——H—>⬮
options -c5
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxCKh-c5', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^0 q^ 2 δ^1 ⬮
2) h^1 q^ 4 δ^1 ⬮——H—>⬮
3) h^1 q^ 4 δ^1 ⬮——H—>⬮
4) h^2 q^ 6 δ^1 ⬮——H—>⬮
5) h^3 q^ 8 δ^1 ⬮——H—>⬮
6) h^4 q^10 δ^1 ⬮——H—>⬮
7) h^4 q^10 δ^1 ⬮——H—>⬮
8) h^6 q^14 δ^1 ⬮——H—>⬮
options -c7
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxCKh-c7', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^0 q^ 2 δ^1 ⬮
2) h^1 q^ 4 δ^1 ⬮——H—>⬮
3) h^1 q^ 4 δ^1 ⬮——H—>⬮
4) h^2 q^ 6 δ^1 ⬮——H—>⬮
5) h^3 q^ 8 δ^1 ⬮——H—>⬮
6) h^4 q^10 δ^1 ⬮——H—>⬮
7) h^4 q^10 δ^1 ⬮——H—>⬮
8) h^6 q^14 δ^1 ⬮——H—>⬮
options -c11
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_4-1/cxCKh-c11', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^0 q^ 2 δ^1 ⬮
2) h^1 q^ 4 δ^1 ⬮——H—>⬮
3) h^1 q^ 4 δ^1 ⬮——H—>⬮
4) h^2 q^ 6 δ^1 ⬮——H—>⬮
5) h^3 q^ 8 δ^1 ⬮——H—>⬮
6) h^4 q^10 δ^1 ⬮——H—>⬮
7) h^4 q^10 δ^1 ⬮——H—>⬮
8) h^6 q^14 δ^1 ⬮——H—>⬮