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Input data and context
% 8_1-1
s.l1.y0.y0.y0.y0.y0.y0.x1.u2
,1
% Symmetry 1 of a 2-bridge knot corresponding to the fraction 13/2 = [6,2] (Sakuma, Prop. 3.6, symmetry 1).
% Simplifies with options '-qs' to y0.y0.r1.x2.y1.y0.y1.y1.y0.y0.y0.y1.y1.y0.y0.y1.y0.y0.y0.y0.y1.y1.y0.y1.y0.y0.y1.y1.y1.y1.y0.y0.y1.y0.y0.y0.y1.y1.u2
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/cxBNr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^36 δ^18 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/cxBNr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^36 δ^18 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/cxBNr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^36 δ^18 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/cxBNr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^36 δ^18 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/cxBNr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^36 δ^18 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/cxKhr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^23 q^71 δ^25/2 ⬯~~S^2~>⬯<— r(∞) q^72 δ_^0
2) h^19 q^65 δ^27/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^70 δ|^13
3) h^15 q^59 δ^29/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^64 δ|^14
4) h^11 q^53 δ^31/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^58 δ|^15
5) h^ 7 q^47 δ^33/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^52 δ|^16
6) h^ 3 q^41 δ^35/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^46 δ|^17
7) h^-1 q^35 δ^37/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^40 δ|^18
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/cxKhr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^23 q^71 δ^25/2 ⬯~~(-S^2)~>⬯<— r(∞) q^72 δ_^0
2) h^19 q^65 δ^27/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^70 δ|^13
3) h^15 q^59 δ^29/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^64 δ|^14
4) h^11 q^53 δ^31/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^58 δ|^15
5) h^ 7 q^47 δ^33/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^52 δ|^16
6) h^ 3 q^41 δ^35/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^46 δ|^17
7) h^-1 q^35 δ^37/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^40 δ|^18
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/cxKhr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^23 q^71 δ^25/2 ⬯~~(-S^2)~>⬯<— r(∞) q^72 δ_^0
2) h^19 q^65 δ^27/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^70 δ|^13
3) h^15 q^59 δ^29/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^64 δ|^14
4) h^11 q^53 δ^31/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^58 δ|^15
5) h^ 7 q^47 δ^33/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^52 δ|^16
6) h^ 3 q^41 δ^35/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^46 δ|^17
7) h^-1 q^35 δ^37/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^40 δ|^18
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/cxKhr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^23 q^71 δ^25/2 ⬯~~(-S^2)~>⬯<— r(∞) q^72 δ_^0
2) h^19 q^65 δ^27/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^70 δ|^13
3) h^15 q^59 δ^29/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^64 δ|^14
4) h^11 q^53 δ^31/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^58 δ|^15
5) h^ 7 q^47 δ^33/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^52 δ|^16
6) h^ 3 q^41 δ^35/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^46 δ|^17
7) h^-1 q^35 δ^37/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^40 δ|^18
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/cxKhr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^23 q^71 δ^25/2 ⬯~~(-S^2)~>⬯<— r(∞) q^72 δ_^0
2) h^19 q^65 δ^27/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^70 δ|^13
3) h^15 q^59 δ^29/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^64 δ|^14
4) h^11 q^53 δ^31/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^58 δ|^15
5) h^ 7 q^47 δ^33/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^52 δ|^16
6) h^ 3 q^41 δ^35/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^46 δ|^17
7) h^-1 q^35 δ^37/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^40 δ|^18
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c0
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/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^-6 q^-12 δ^0 ⬮——H—>⬮
3) h^-4 q^ -8 δ^0 ⬮——H—>⬮
4) h^-3 q^ -6 δ^0 ⬮——H—>⬮
5) h^-2 q^ -4 δ^0 ⬮——H—>⬮
6) h^-1 q^ -2 δ^0 ⬮——H—>⬮
7) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
options -c2
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/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^-6 q^-12 δ^0 ⬮——H—>⬮
3) h^-4 q^ -8 δ^0 ⬮——H—>⬮
4) h^-3 q^ -6 δ^0 ⬮——H—>⬮
5) h^-2 q^ -4 δ^0 ⬮——H—>⬮
6) h^-1 q^ -2 δ^0 ⬮——H—>⬮
7) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
options -c3
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/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^-6 q^-12 δ^0 ⬮——H—>⬮
3) h^-4 q^ -8 δ^0 ⬮——H—>⬮
4) h^-3 q^ -6 δ^0 ⬮——H—>⬮
5) h^-2 q^ -4 δ^0 ⬮——H—>⬮
6) h^-1 q^ -2 δ^0 ⬮——H—>⬮
7) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
options -c5
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/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^-6 q^-12 δ^0 ⬮——H—>⬮
3) h^-4 q^ -8 δ^0 ⬮——H—>⬮
4) h^-3 q^ -6 δ^0 ⬮——H—>⬮
5) h^-2 q^ -4 δ^0 ⬮——H—>⬮
6) h^-1 q^ -2 δ^0 ⬮——H—>⬮
7) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
options -c7
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/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^-6 q^-12 δ^0 ⬮——H—>⬮
3) h^-4 q^ -8 δ^0 ⬮——H—>⬮
4) h^-3 q^ -6 δ^0 ⬮——H—>⬮
5) h^-2 q^ -4 δ^0 ⬮——H—>⬮
6) h^-1 q^ -2 δ^0 ⬮——H—>⬮
7) h^ 1 q^ 2 δ^0 ⬮——H—>⬮
options -c11
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-1/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^-6 q^-12 δ^0 ⬮——H—>⬮
3) h^-4 q^ -8 δ^0 ⬮——H—>⬮
4) h^-3 q^ -6 δ^0 ⬮——H—>⬮
5) h^-2 q^ -4 δ^0 ⬮——H—>⬮
6) h^-1 q^ -2 δ^0 ⬮——H—>⬮
7) h^ 1 q^ 2 δ^0 ⬮——H—>⬮