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Input data and context
% 7_2-2
s.l1.y0.y0.y1.y1.y1.u2
,1
% Symmetry 2 of a 2-bridge knot corresponding to the fraction 11/2 = [6,-2] (Sakuma, Prop. 3.6, Case (1), symmetry 2).
% Simplifies with options '-qs' to r2.y1.r2.y1.x3.y2.y1.y2.y1.y2.y2.y1.y2.y2.y2.y4.y3.y2.y4.y3.y3.y2.x1.y4.y4.y3.x0.y1.u2.y2.x1.y0.u2.y0
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/cxBNr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 0 q^10 δ^5 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
2) h^ 2 q^12 δ^4 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-2 q^ 6 δ^5 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/cxBNr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 0 q^10 δ^5 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
2) h^ 2 q^12 δ^4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-2 q^ 6 δ^5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/cxBNr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 0 q^10 δ^5 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
2) h^ 2 q^12 δ^4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-2 q^ 6 δ^5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/cxBNr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 0 q^10 δ^5 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
2) h^ 2 q^12 δ^4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-2 q^ 6 δ^5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/cxBNr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 0 q^10 δ^5 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
2) h^ 2 q^12 δ^4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-2 q^ 6 δ^5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/cxKhr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 3 q^15 δ^ 9/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^96/5 δ|^4
2) h^ 1 q^11 δ^ 9/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^4
3) h^ 2 q^13 δ^ 9/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^4
4) h^-3 q^ 5 δ^11/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^10 δ|^5
5) h^-2 q^ 7 δ^11/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^12 δ|^5
6) h^-1 q^ 9 δ^11/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^14 δ|^5
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/cxKhr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 3 q^15 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^96/5 δ|^4
2) h^ 1 q^11 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^4
3) h^ 2 q^13 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^4
4) h^-3 q^ 5 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^10 δ|^5
5) h^-2 q^ 7 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^12 δ|^5
6) h^-1 q^ 9 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^14 δ|^5
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/cxKhr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 3 q^15 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^96/5 δ|^4
2) h^ 1 q^11 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^4
3) h^ 2 q^13 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^4
4) h^-3 q^ 5 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^10 δ|^5
5) h^-2 q^ 7 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^12 δ|^5
6) h^-1 q^ 9 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^14 δ|^5
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/cxKhr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 3 q^15 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^96/5 δ|^4
2) h^ 1 q^11 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^4
3) h^ 2 q^13 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^4
4) h^-3 q^ 5 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^10 δ|^5
5) h^-2 q^ 7 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^12 δ|^5
6) h^-1 q^ 9 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^14 δ|^5
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/cxKhr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 3 q^15 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^96/5 δ|^4
2) h^ 1 q^11 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^4
3) h^ 2 q^13 δ^ 9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^4
4) h^-3 q^ 5 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^10 δ|^5
5) h^-2 q^ 7 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^12 δ|^5
6) h^-1 q^ 9 δ^11/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^14 δ|^5
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c0
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/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^-7 q^-16 δ^-1 ⬮——H—>⬮
3) h^-5 q^-12 δ^-1 ⬮——H—>⬮
4) h^-4 q^-10 δ^-1 ⬮——H—>⬮
5) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
6) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c2
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/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^-7 q^-16 δ^-1 ⬮——H—>⬮
3) h^-5 q^-12 δ^-1 ⬮——H—>⬮
4) h^-4 q^-10 δ^-1 ⬮——H—>⬮
5) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
6) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c3
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/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^-7 q^-16 δ^-1 ⬮——H—>⬮
3) h^-5 q^-12 δ^-1 ⬮——H—>⬮
4) h^-4 q^-10 δ^-1 ⬮——H—>⬮
5) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
6) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c5
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/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^-7 q^-16 δ^-1 ⬮——H—>⬮
3) h^-5 q^-12 δ^-1 ⬮——H—>⬮
4) h^-4 q^-10 δ^-1 ⬮——H—>⬮
5) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
6) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c7
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/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^-7 q^-16 δ^-1 ⬮——H—>⬮
3) h^-5 q^-12 δ^-1 ⬮——H—>⬮
4) h^-4 q^-10 δ^-1 ⬮——H—>⬮
5) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
6) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c11
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/7_2-2/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^-7 q^-16 δ^-1 ⬮——H—>⬮
3) h^-5 q^-12 δ^-1 ⬮——H—>⬮
4) h^-4 q^-10 δ^-1 ⬮——H—>⬮
5) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
6) h^-2 q^ -6 δ^-1 ⬮——H—>⬮