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Input data and context
% 8_2-1
s.l1.y0.y0.y1.y0.y0.y1.y0.y0.x1.u2
,1
% Symmetry 1 of a 2-bridge knot corresponding to the fraction 17/14 = [2,-2,2,-2,2,2] (Sakuma, Prop. 3.6, symmetry 1).
% Simplifies with options '-qs' to l1.y2.l3.y4.y4.x2.y3.y4.y4.y3.y2.x0.x1.y0.y0.u2.y1.y2.y2.y2.y1.y2.y2.y1.y1.y1.y1.y2.x0.u1.y0.y0.y0
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/cxBNr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^4 q^26 δ^ 9 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^5 q^28 δ^ 9 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^1 q^22 δ^10 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^0 q^20 δ^10 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/cxBNr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^4 q^26 δ^ 9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^5 q^28 δ^ 9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^1 q^22 δ^10 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^0 q^20 δ^10 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/cxBNr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^4 q^26 δ^ 9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^5 q^28 δ^ 9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^1 q^22 δ^10 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^0 q^20 δ^10 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/cxBNr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^4 q^26 δ^ 9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^5 q^28 δ^ 9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^1 q^22 δ^10 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^0 q^20 δ^10 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/cxBNr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^4 q^26 δ^ 9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^5 q^28 δ^ 9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^1 q^22 δ^10 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^0 q^20 δ^10 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/cxKhr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 3 q^25 δ^19/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^30 δ|^9
2) h^ 3 q^25 δ^19/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^30 δ|^9
3) h^ 4 q^27 δ^19/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^9
4) h^ 4 q^27 δ^19/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^9
5) h^ 5 q^29 δ^19/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^34 δ|^9
6) h^-1 q^19 δ^21/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^24 δ|^10
7) h^ 0 q^21 δ^21/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^10
8) h^ 1 q^23 δ^21/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^28 δ|^10
9) h^ 7 q^31 δ^17/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/8) q^352/9 δ|^8
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/cxKhr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 3 q^25 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^30 δ|^9
2) h^ 3 q^25 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^30 δ|^9
3) h^ 4 q^27 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^9
4) h^ 4 q^27 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^9
5) h^ 5 q^29 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^34 δ|^9
6) h^-1 q^19 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^24 δ|^10
7) h^ 0 q^21 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^10
8) h^ 1 q^23 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^28 δ|^10
9) h^ 7 q^31 δ^17/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/8) q^352/9 δ|^8
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/cxKhr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 3 q^25 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^30 δ|^9
2) h^ 3 q^25 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^30 δ|^9
3) h^ 4 q^27 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^9
4) h^ 4 q^27 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^9
5) h^ 5 q^29 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^34 δ|^9
6) h^-1 q^19 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^24 δ|^10
7) h^ 0 q^21 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^10
8) h^ 1 q^23 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^28 δ|^10
9) h^ 7 q^31 δ^17/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/8) q^352/9 δ|^8
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/cxKhr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 3 q^25 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^30 δ|^9
2) h^ 3 q^25 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^30 δ|^9
3) h^ 4 q^27 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^9
4) h^ 4 q^27 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^9
5) h^ 5 q^29 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^34 δ|^9
6) h^-1 q^19 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^24 δ|^10
7) h^ 0 q^21 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^10
8) h^ 1 q^23 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^28 δ|^10
9) h^ 7 q^31 δ^17/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/8) q^352/9 δ|^8
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/cxKhr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ 3 q^25 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^30 δ|^9
2) h^ 3 q^25 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^30 δ|^9
3) h^ 4 q^27 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^9
4) h^ 4 q^27 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^32 δ|^9
5) h^ 5 q^29 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^34 δ|^9
6) h^-1 q^19 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^24 δ|^10
7) h^ 0 q^21 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^26 δ|^10
8) h^ 1 q^23 δ^21/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^28 δ|^10
9) h^ 7 q^31 δ^17/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/8) q^352/9 δ|^8
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c0
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/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^-6 q^-16 δ^-2 ⬮——H—>⬮
3) h^-5 q^-14 δ^-2 ⬮——H—>⬮
4) h^-4 q^-12 δ^-2 ⬮——H—>⬮
5) h^-3 q^-10 δ^-2 ⬮——H—>⬮
6) h^-3 q^-10 δ^-2 ⬮——H—>⬮
7) h^-2 q^ -8 δ^-2 ⬮——H—>⬮
8) h^-1 q^ -6 δ^-2 ⬮——H—>⬮
9) h^ 1 q^ -2 δ^-2 ⬮——H—>⬮
options -c2
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/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^-6 q^-16 δ^-2 ⬮——H—>⬮
3) h^-5 q^-14 δ^-2 ⬮——H—>⬮
4) h^-4 q^-12 δ^-2 ⬮——H—>⬮
5) h^-3 q^-10 δ^-2 ⬮——H—>⬮
6) h^-3 q^-10 δ^-2 ⬮——H—>⬮
7) h^-2 q^ -8 δ^-2 ⬮——H—>⬮
8) h^-1 q^ -6 δ^-2 ⬮——H—>⬮
9) h^ 1 q^ -2 δ^-2 ⬮——H—>⬮
options -c3
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/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^-6 q^-16 δ^-2 ⬮——H—>⬮
3) h^-5 q^-14 δ^-2 ⬮——H—>⬮
4) h^-4 q^-12 δ^-2 ⬮——H—>⬮
5) h^-3 q^-10 δ^-2 ⬮——H—>⬮
6) h^-3 q^-10 δ^-2 ⬮——H—>⬮
7) h^-2 q^ -8 δ^-2 ⬮——H—>⬮
8) h^-1 q^ -6 δ^-2 ⬮——H—>⬮
9) h^ 1 q^ -2 δ^-2 ⬮——H—>⬮
options -c5
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/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^-6 q^-16 δ^-2 ⬮——H—>⬮
3) h^-5 q^-14 δ^-2 ⬮——H—>⬮
4) h^-4 q^-12 δ^-2 ⬮——H—>⬮
5) h^-3 q^-10 δ^-2 ⬮——H—>⬮
6) h^-3 q^-10 δ^-2 ⬮——H—>⬮
7) h^-2 q^ -8 δ^-2 ⬮——H—>⬮
8) h^-1 q^ -6 δ^-2 ⬮——H—>⬮
9) h^ 1 q^ -2 δ^-2 ⬮——H—>⬮
options -c7
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/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^-6 q^-16 δ^-2 ⬮——H—>⬮
3) h^-5 q^-14 δ^-2 ⬮——H—>⬮
4) h^-4 q^-12 δ^-2 ⬮——H—>⬮
5) h^-3 q^-10 δ^-2 ⬮——H—>⬮
6) h^-3 q^-10 δ^-2 ⬮——H—>⬮
7) h^-2 q^ -8 δ^-2 ⬮——H—>⬮
8) h^-1 q^ -6 δ^-2 ⬮——H—>⬮
9) h^ 1 q^ -2 δ^-2 ⬮——H—>⬮
options -c11
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_2-1/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^-6 q^-16 δ^-2 ⬮——H—>⬮
3) h^-5 q^-14 δ^-2 ⬮——H—>⬮
4) h^-4 q^-12 δ^-2 ⬮——H—>⬮
5) h^-3 q^-10 δ^-2 ⬮——H—>⬮
6) h^-3 q^-10 δ^-2 ⬮——H—>⬮
7) h^-2 q^ -8 δ^-2 ⬮——H—>⬮
8) h^-1 q^ -6 δ^-2 ⬮——H—>⬮
9) h^ 1 q^ -2 δ^-2 ⬮——H—>⬮