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Input data and context
% 5_2-1
s.l1.y0.y0.y0.y0.y1.u2
,1
% Symmetry 1 of a 2-bridge knot corresponding to the fraction 7/2 = [4,-2] (Sakuma, Prop. 3.6, symmetry 1).
% Simplifies with options '-qs' to r1.r2.y3.y3.x4.x3.y2.y1.y1.y1.y1.y2.y1.y1.y2.y2.y2.y1.y1.y2.y1.x3.u4.x0.x1.u2.y0.y0.y0.y0
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/cxBNr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^22 δ^11 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/cxBNr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^22 δ^11 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/cxBNr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^22 δ^11 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/cxBNr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^22 δ^11 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/cxBNr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^22 δ^11 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/cxKhr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^11 q^39 δ^17/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^216/5 δ|^8
2) h^ 7 q^33 δ^19/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^38 δ|^9
3) h^ 3 q^27 δ^21/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^10
4) h^-1 q^21 δ^23/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^11
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/cxKhr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^11 q^39 δ^17/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^216/5 δ|^8
2) h^ 7 q^33 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^38 δ|^9
3) h^ 3 q^27 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^10
4) h^-1 q^21 δ^23/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^11
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/cxKhr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^11 q^39 δ^17/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^216/5 δ|^8
2) h^ 7 q^33 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^38 δ|^9
3) h^ 3 q^27 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^10
4) h^-1 q^21 δ^23/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^11
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/cxKhr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^11 q^39 δ^17/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^216/5 δ|^8
2) h^ 7 q^33 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^38 δ|^9
3) h^ 3 q^27 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^10
4) h^-1 q^21 δ^23/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^11
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/cxKhr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^11 q^39 δ^17/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^216/5 δ|^8
2) h^ 7 q^33 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^38 δ|^9
3) h^ 3 q^27 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^10
4) h^-1 q^21 δ^23/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^11
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c0
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/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^-5 q^-12 δ^-1 ⬮——H—>⬮
3) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
4) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c2
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/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^-5 q^-12 δ^-1 ⬮——H—>⬮
3) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
4) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c3
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/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^-5 q^-12 δ^-1 ⬮——H—>⬮
3) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
4) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c5
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/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^-5 q^-12 δ^-1 ⬮——H—>⬮
3) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
4) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c7
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/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^-5 q^-12 δ^-1 ⬮——H—>⬮
3) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
4) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c11
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/5_2-1/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^-5 q^-12 δ^-1 ⬮——H—>⬮
3) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
4) h^-2 q^ -6 δ^-1 ⬮——H—>⬮