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Input data and context
% 8_1-2
s.l1.x0.x0.y1.y1.y1.u2
,1
% Symmetry 2 of a 2-bridge knot corresponding to the fraction 13/2 = [6,2] (Sakuma, Prop. 3.6, Case (1), symmetry 2).
% Simplifies with options '-qs' to r2.x1.r3.x2.x2.x1.x1.x2.x2.y3.y4.x1.y2.y4.y3.y4.y2.x1.x0.y4.y3.x2.u3.x1.u2.y0
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-2/cxBNr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -7 q^-24 δ^-5 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-11 q^-30 δ^-4 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ -8 q^-24 δ^-4 ⬯<—D——⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-2/cxBNr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -7 q^-24 δ^-5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-11 q^-30 δ^-4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ -8 q^-24 δ^-4 ⬯<—D——⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-2/cxBNr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -7 q^-24 δ^-5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-11 q^-30 δ^-4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ -8 q^-24 δ^-4 ⬯<—D——⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-2/cxBNr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -7 q^-24 δ^-5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-11 q^-30 δ^-4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ -8 q^-24 δ^-4 ⬯<—D——⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-2/cxBNr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -7 q^-24 δ^-5 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-11 q^-30 δ^-4 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ -8 q^-24 δ^-4 ⬯<—D——⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-2/cxKhr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -9 q^-25 δ^-7/2 ⬯~~S^2~>⬯<— r(∞) q^-24 δ_^0
2) h^ -8 q^-25 δ^-9/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-20 δ|^-5
3) h^ -7 q^-23 δ^-9/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-18 δ|^-5
4) h^ -6 q^-21 δ^-9/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-16 δ|^-5
5) h^-12 q^-31 δ^-7/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-26 δ|^-4
6) h^-11 q^-29 δ^-7/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-24 δ|^-4
7) h^-10 q^-27 δ^-7/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-22 δ|^-4
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-2/cxKhr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -9 q^-25 δ^-7/2 ⬯~~(-S^2)~>⬯<— r(∞) q^-24 δ_^0
2) h^ -8 q^-25 δ^-9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-20 δ|^-5
3) h^ -7 q^-23 δ^-9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-18 δ|^-5
4) h^ -6 q^-21 δ^-9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-16 δ|^-5
5) h^-12 q^-31 δ^-7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-26 δ|^-4
6) h^-11 q^-29 δ^-7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-24 δ|^-4
7) h^-10 q^-27 δ^-7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-22 δ|^-4
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-2/cxKhr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -9 q^-25 δ^-7/2 ⬯~~(-S^2)~>⬯<— r(∞) q^-24 δ_^0
2) h^ -8 q^-25 δ^-9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-20 δ|^-5
3) h^ -7 q^-23 δ^-9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-18 δ|^-5
4) h^ -6 q^-21 δ^-9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-16 δ|^-5
5) h^-12 q^-31 δ^-7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-26 δ|^-4
6) h^-11 q^-29 δ^-7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-24 δ|^-4
7) h^-10 q^-27 δ^-7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-22 δ|^-4
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-2/cxKhr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -9 q^-25 δ^-7/2 ⬯~~(-S^2)~>⬯<— r(∞) q^-24 δ_^0
2) h^ -8 q^-25 δ^-9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-20 δ|^-5
3) h^ -7 q^-23 δ^-9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-18 δ|^-5
4) h^ -6 q^-21 δ^-9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-16 δ|^-5
5) h^-12 q^-31 δ^-7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-26 δ|^-4
6) h^-11 q^-29 δ^-7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-24 δ|^-4
7) h^-10 q^-27 δ^-7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-22 δ|^-4
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-2/cxKhr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^ -9 q^-25 δ^-7/2 ⬯~~(-S^2)~>⬯<— r(∞) q^-24 δ_^0
2) h^ -8 q^-25 δ^-9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-20 δ|^-5
3) h^ -7 q^-23 δ^-9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-18 δ|^-5
4) h^ -6 q^-21 δ^-9/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-16 δ|^-5
5) h^-12 q^-31 δ^-7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-26 δ|^-4
6) h^-11 q^-29 δ^-7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-24 δ|^-4
7) h^-10 q^-27 δ^-7/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-22 δ|^-4
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c0
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/8_1-2/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^-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_1-2/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^-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_1-2/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^-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_1-2/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^-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_1-2/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^-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_1-2/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^-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—>⬮