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Input data and context
% 6_3-2
s.r1.x0.x0.x1.y0.y0.y1.u2
,1
% Symmetry 2 of a 2-bridge knot corresponding to the fraction 13/8 = [2,-2,-2,2] (Sakuma, Prop. 3.6, Case (1), symmetry 2).
% Simplifies with options '-qs' to l1.y2.l2.y3.x2.x1.y0.u1.x0.y1.y2.y1.y2.y1.y1.y2.y2.x0.u1
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxBNr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^7 q^22 δ^4 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^3 q^16 δ^5 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^0 q^12 δ^6 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxBNr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^7 q^22 δ^4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^3 q^16 δ^5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^0 q^12 δ^6 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxBNr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^7 q^22 δ^4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^3 q^16 δ^5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^0 q^12 δ^6 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxBNr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^7 q^22 δ^4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^3 q^16 δ^5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^0 q^12 δ^6 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxBNr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^7 q^22 δ^4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^3 q^16 δ^5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^0 q^12 δ^6 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxKhr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 7 q^23 δ^ 9/2 ⬯~~S^2~>⬯<— r(∞) q^24 δ_^0
2) h^ 6 q^21 δ^ 9/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^4
3) h^ 7 q^23 δ^ 9/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^28 δ|^4
4) h^ 2 q^15 δ^11/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^20 δ|^5
5) h^ 3 q^17 δ^11/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^5
6) h^ 3 q^17 δ^11/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^5
7) h^-1 q^11 δ^13/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^6
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxKhr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 7 q^23 δ^ 9/2 ⬯~~(-S^2)~>⬯<— r(∞) q^24 δ_^0
2) h^ 6 q^21 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^4
3) h^ 7 q^23 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^28 δ|^4
4) h^ 2 q^15 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^20 δ|^5
5) h^ 3 q^17 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^5
6) h^ 3 q^17 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^5
7) h^-1 q^11 δ^13/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^6
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxKhr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 7 q^23 δ^ 9/2 ⬯~~(-S^2)~>⬯<— r(∞) q^24 δ_^0
2) h^ 6 q^21 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^4
3) h^ 7 q^23 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^28 δ|^4
4) h^ 2 q^15 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^20 δ|^5
5) h^ 3 q^17 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^5
6) h^ 3 q^17 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^5
7) h^-1 q^11 δ^13/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^6
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxKhr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 7 q^23 δ^ 9/2 ⬯~~(-S^2)~>⬯<— r(∞) q^24 δ_^0
2) h^ 6 q^21 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^4
3) h^ 7 q^23 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^28 δ|^4
4) h^ 2 q^15 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^20 δ|^5
5) h^ 3 q^17 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^5
6) h^ 3 q^17 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^5
7) h^-1 q^11 δ^13/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^6
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxKhr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 7 q^23 δ^ 9/2 ⬯~~(-S^2)~>⬯<— r(∞) q^24 δ_^0
2) h^ 6 q^21 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^4
3) h^ 7 q^23 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^28 δ|^4
4) h^ 2 q^15 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^20 δ|^5
5) h^ 3 q^17 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^5
6) h^ 3 q^17 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^22 δ|^5
7) h^-1 q^11 δ^13/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^6
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c0
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxCKh-c0', generated by kht, version v0.1, on Sun Mar 7 15:45:53 2021 GMT
1) h^ 0 q^ 0 δ^0 ⬮
2) h^-3 q^-6 δ^0 ⬮——H—>⬮
3) h^-2 q^-4 δ^0 ⬮——H—>⬮
4) h^-1 q^-2 δ^0 ⬮——H—>⬮
5) h^ 0 q^ 0 δ^0 ⬮——H—>⬮
6) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
7) h^ 2 q^ 4 δ^0 ⬮——H—>⬮
options -c2
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxCKh-c2', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ 0 δ^0 ⬮
2) h^-3 q^-6 δ^0 ⬮——H—>⬮
3) h^-2 q^-4 δ^0 ⬮——H—>⬮
4) h^-1 q^-2 δ^0 ⬮——H—>⬮
5) h^ 0 q^ 0 δ^0 ⬮——H—>⬮
6) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
7) h^ 2 q^ 4 δ^0 ⬮——H—>⬮
options -c3
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxCKh-c3', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ 0 δ^0 ⬮
2) h^-3 q^-6 δ^0 ⬮——H—>⬮
3) h^-2 q^-4 δ^0 ⬮——H—>⬮
4) h^-1 q^-2 δ^0 ⬮——H—>⬮
5) h^ 0 q^ 0 δ^0 ⬮——H—>⬮
6) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
7) h^ 2 q^ 4 δ^0 ⬮——H—>⬮
options -c5
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxCKh-c5', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ 0 δ^0 ⬮
2) h^-3 q^-6 δ^0 ⬮——H—>⬮
3) h^-2 q^-4 δ^0 ⬮——H—>⬮
4) h^-1 q^-2 δ^0 ⬮——H—>⬮
5) h^ 0 q^ 0 δ^0 ⬮——H—>⬮
6) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
7) h^ 2 q^ 4 δ^0 ⬮——H—>⬮
options -c7
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxCKh-c7', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ 0 δ^0 ⬮
2) h^-3 q^-6 δ^0 ⬮——H—>⬮
3) h^-2 q^-4 δ^0 ⬮——H—>⬮
4) h^-1 q^-2 δ^0 ⬮——H—>⬮
5) h^ 0 q^ 0 δ^0 ⬮——H—>⬮
6) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
7) h^ 2 q^ 4 δ^0 ⬮——H—>⬮
options -c11
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/6_3-2/cxCKh-c11', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ 0 δ^0 ⬮
2) h^-3 q^-6 δ^0 ⬮——H—>⬮
3) h^-2 q^-4 δ^0 ⬮——H—>⬮
4) h^-1 q^-2 δ^0 ⬮——H—>⬮
5) h^ 0 q^ 0 δ^0 ⬮——H—>⬮
6) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
7) h^ 2 q^ 4 δ^0 ⬮——H—>⬮