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Input data and context
% 7_3-1
s.r1.x0.x0.x0.x0.x1.x0.x0.x1.u2
,1
% Symmetry 1 of a 2-bridge knot corresponding to the fraction 13/-4 = [-4,2,-2,2] (Sakuma, Prop. 3.6, symmetry 1).
% Simplifies with options '-qs' to l1.y2.l3.x2.x1.x1.x4.x2.x2.x2.x1.x2.x1.x2.x2.x1.x2.x2.x2.x4.x4.y3.y4.x1.x2.x1.x3.x2.x3.y4.u3.x1.x1.x1.x2.y0.u1.x0.x0.x0
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxBNr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-8 q^-23 δ^-7/2 ⬮——D—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯
2) h^ 6 q^ 0 δ^ -6 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 2 q^ -6 δ^ -5 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^-2 q^-12 δ^ -4 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxBNr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-8 q^-23 δ^-7/2 ⬮——D—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯
2) h^ 6 q^ 0 δ^ -6 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 2 q^ -6 δ^ -5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^-2 q^-12 δ^ -4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxBNr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-8 q^-23 δ^-7/2 ⬮——D—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯
2) h^ 6 q^ 0 δ^ -6 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 2 q^ -6 δ^ -5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^-2 q^-12 δ^ -4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxBNr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-8 q^-23 δ^-7/2 ⬮——D—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯
2) h^ 6 q^ 0 δ^ -6 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 2 q^ -6 δ^ -5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^-2 q^-12 δ^ -4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxBNr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-8 q^-23 δ^-7/2 ⬮——D—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯
2) h^ 6 q^ 0 δ^ -6 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 2 q^ -6 δ^ -5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^-2 q^-12 δ^ -4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxKhr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 5 q^ -1 δ^-11/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^4 δ|^-6
2) h^ 6 q^ 1 δ^-11/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^6 δ|^-6
3) h^ 1 q^ -7 δ^ -9/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^-5
4) h^ 2 q^ -5 δ^ -9/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^-5
5) h^-3 q^-13 δ^ -7/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^-4
6) h^-2 q^-11 δ^ -7/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^-4
7) h^-9 q^-24 δ^ -3 ⬮~~S^2~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<— r(-1/8) q^-136/9 δ|^-3
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxKhr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 5 q^ -1 δ^-11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^4 δ|^-6
2) h^ 6 q^ 1 δ^-11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^6 δ|^-6
3) h^ 1 q^ -7 δ^ -9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^-5
4) h^ 2 q^ -5 δ^ -9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^-5
5) h^-3 q^-13 δ^ -7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^-4
6) h^-2 q^-11 δ^ -7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^-4
7) h^-9 q^-24 δ^ -3 ⬮~~(-S^2)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<— r(-1/8) q^-136/9 δ|^-3
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxKhr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 5 q^ -1 δ^-11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^4 δ|^-6
2) h^ 6 q^ 1 δ^-11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^6 δ|^-6
3) h^ 1 q^ -7 δ^ -9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^-5
4) h^ 2 q^ -5 δ^ -9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^-5
5) h^-3 q^-13 δ^ -7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^-4
6) h^-2 q^-11 δ^ -7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^-4
7) h^-9 q^-24 δ^ -3 ⬮~~(-S^2)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<— r(-1/8) q^-136/9 δ|^-3
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxKhr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 5 q^ -1 δ^-11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^4 δ|^-6
2) h^ 6 q^ 1 δ^-11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^6 δ|^-6
3) h^ 1 q^ -7 δ^ -9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^-5
4) h^ 2 q^ -5 δ^ -9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^-5
5) h^-3 q^-13 δ^ -7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^-4
6) h^-2 q^-11 δ^ -7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^-4
7) h^-9 q^-24 δ^ -3 ⬮~~(-S^2)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<— r(-1/8) q^-136/9 δ|^-3
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxKhr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 5 q^ -1 δ^-11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^4 δ|^-6
2) h^ 6 q^ 1 δ^-11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^6 δ|^-6
3) h^ 1 q^ -7 δ^ -9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^-5
4) h^ 2 q^ -5 δ^ -9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^-5
5) h^-3 q^-13 δ^ -7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^-4
6) h^-2 q^-11 δ^ -7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^-4
7) h^-9 q^-24 δ^ -3 ⬮~~(-S^2)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<— r(-1/8) q^-136/9 δ|^-3
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c0
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxCKh-c0', generated by kht, version v0.1, on Sun Mar 7 15:45:53 2021 GMT
1) h^0 q^ 4 δ^2 ⬮
2) h^1 q^ 6 δ^2 ⬮——H—>⬮
3) h^2 q^ 8 δ^2 ⬮——H—>⬮
4) h^3 q^10 δ^2 ⬮——H—>⬮
5) h^4 q^12 δ^2 ⬮——H—>⬮
6) h^4 q^12 δ^2 ⬮——H—>⬮
7) h^6 q^16 δ^2 ⬮——H—>⬮
options -c2
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxCKh-c2', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^0 q^ 4 δ^2 ⬮
2) h^1 q^ 6 δ^2 ⬮——H—>⬮
3) h^2 q^ 8 δ^2 ⬮——H—>⬮
4) h^3 q^10 δ^2 ⬮——H—>⬮
5) h^4 q^12 δ^2 ⬮——H—>⬮
6) h^4 q^12 δ^2 ⬮——H—>⬮
7) h^6 q^16 δ^2 ⬮——H—>⬮
options -c3
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxCKh-c3', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^0 q^ 4 δ^2 ⬮
2) h^1 q^ 6 δ^2 ⬮——H—>⬮
3) h^2 q^ 8 δ^2 ⬮——H—>⬮
4) h^3 q^10 δ^2 ⬮——H—>⬮
5) h^4 q^12 δ^2 ⬮——H—>⬮
6) h^4 q^12 δ^2 ⬮——H—>⬮
7) h^6 q^16 δ^2 ⬮——H—>⬮
options -c5
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxCKh-c5', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^0 q^ 4 δ^2 ⬮
2) h^1 q^ 6 δ^2 ⬮——H—>⬮
3) h^2 q^ 8 δ^2 ⬮——H—>⬮
4) h^3 q^10 δ^2 ⬮——H—>⬮
5) h^4 q^12 δ^2 ⬮——H—>⬮
6) h^4 q^12 δ^2 ⬮——H—>⬮
7) h^6 q^16 δ^2 ⬮——H—>⬮
options -c7
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxCKh-c7', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^0 q^ 4 δ^2 ⬮
2) h^1 q^ 6 δ^2 ⬮——H—>⬮
3) h^2 q^ 8 δ^2 ⬮——H—>⬮
4) h^3 q^10 δ^2 ⬮——H—>⬮
5) h^4 q^12 δ^2 ⬮——H—>⬮
6) h^4 q^12 δ^2 ⬮——H—>⬮
7) h^6 q^16 δ^2 ⬮——H—>⬮
options -c11
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_3-1/cxCKh-c11', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^0 q^ 4 δ^2 ⬮
2) h^1 q^ 6 δ^2 ⬮——H—>⬮
3) h^2 q^ 8 δ^2 ⬮——H—>⬮
4) h^3 q^10 δ^2 ⬮——H—>⬮
5) h^4 q^12 δ^2 ⬮——H—>⬮
6) h^4 q^12 δ^2 ⬮——H—>⬮
7) h^6 q^16 δ^2 ⬮——H—>⬮