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Input data and context
% 8_15-1
s.r1.x0.x0.y2.x1.x1.u2
,1
% Simplifies with options '-q' to l1.y2.l3.x2.x2.x1.x1.l1.y2.x4.y3.x4.l4.x3.x2.y4.x7.u5.x2.y0.u1.x4.y0.y1.u2.x1.y2.y2.u0
% Simplifies with options '-qs' to l2.x1.l2.y3.x2.x1.y2.x1.l2.x4.y3.x4.x5.l5.y4.y4.u3.x1.y0.x2.x2.u1.y0.y0.x2.u1.y0.y1.u2
% Simplifies with options '-qs' to l1.y2.l2.y3.y4.y1.x2.x1.x1.x2.l3.x4.y3.l3.x2.x1.y3.u4.x3.x2.x2.y0.u1.y1.y0.x3.x4.u2.u1
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c2-qs
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxBNr-c2-qs', generated by kht, version v0.1, on Sun Mar 7 19:25:23 2021 GMT
1) h^ 0 q^ -2 δ^-1 ⬯<~S~~⬮<—⬮<~⬮<—⬮<~⬯—>⬯~>⬮—>⬮~>⬮—>⬮
2) h^-2 q^ -6 δ^-1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^-6 q^-12 δ^ 0 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^-9 q^-16 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c3-qs
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxBNr-c3-qs', generated by kht, version v0.1, on Sun Mar 7 19:25:23 2021 GMT
1) h^-4 q^ -8 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
2) h^-9 q^-16 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
3) h^ 0 q^ -2 δ^-1 ⬯<~S~~⬮<—⬮<~⬮<—⬮<~⬯—>⬯~>⬮—>⬮~>⬮—>⬮
4) h^-2 q^ -6 δ^-1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c5-qs
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxBNr-c5-qs', generated by kht, version v0.1, on Sun Mar 7 19:25:23 2021 GMT
1) h^-4 q^ -8 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
2) h^-9 q^-16 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
3) h^ 0 q^ -2 δ^-1 ⬯<~S~~⬮<—⬮<~⬮<—⬮<~⬯—>⬯~>⬮—>⬮~>⬮—>⬮
4) h^-2 q^ -6 δ^-1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c7-qs
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxBNr-c7-qs', generated by kht, version v0.1, on Sun Mar 7 19:25:23 2021 GMT
1) h^-4 q^ -8 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
2) h^-9 q^-16 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
3) h^ 0 q^ -2 δ^-1 ⬯<~S~~⬮<—⬮<~⬮<—⬮<~⬯—>⬯~>⬮—>⬮~>⬮—>⬮
4) h^-2 q^ -6 δ^-1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c11-qs
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxBNr-c11-qs', generated by kht, version v0.1, on Sun Mar 7 19:25:23 2021 GMT
1) h^-4 q^ -8 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
2) h^-9 q^-16 δ^ 1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
3) h^ 0 q^ -2 δ^-1 ⬯<~S~~⬮<—⬮<~⬮<—⬮<~⬯—>⬯~>⬮—>⬮~>⬮—>⬮
4) h^-2 q^ -6 δ^-1 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c2-qs
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxKhr-c2-qs', generated by kht, version v0.1, on Sun Mar 7 19:25:23 2021 GMT
1) h^ -5 q^ -9 δ^ 1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^-24/5 δ|^0
2) h^ -3 q^ -7 δ^-1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^-1
3) h^ -2 q^ -5 δ^-1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^-1
4) h^ -7 q^-13 δ^ 1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-8 δ|^0
5) h^ -6 q^-11 δ^ 1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^0
6) h^ -6 q^-11 δ^ 1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^0
7) h^-10 q^-17 δ^ 3/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-12 δ|^1
8) h^ -9 q^-15 δ^ 3/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-10 δ|^1
options -c3-qs
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxKhr-c3-qs', generated by kht, version v0.1, on Sun Mar 7 19:25:23 2021 GMT
1) h^ -5 q^ -9 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-6 δ|^0
2) h^ -4 q^ -7 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-4 δ|^0
3) h^-10 q^-17 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-14 δ|^1
4) h^ -9 q^-15 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-12 δ|^1
5) h^ -5 q^ -9 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^-24/5 δ|^0
6) h^ -3 q^ -7 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^-1
7) h^ -2 q^ -5 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^-1
8) h^ -6 q^-11 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^0
options -c5-qs
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxKhr-c5-qs', generated by kht, version v0.1, on Sun Mar 7 19:25:23 2021 GMT
1) h^ -5 q^ -9 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-6 δ|^0
2) h^ -4 q^ -7 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-4 δ|^0
3) h^-10 q^-17 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-14 δ|^1
4) h^ -9 q^-15 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-12 δ|^1
5) h^ -5 q^ -9 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^-24/5 δ|^0
6) h^ -3 q^ -7 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^-1
7) h^ -2 q^ -5 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^-1
8) h^ -6 q^-11 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^0
options -c7-qs
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxKhr-c7-qs', generated by kht, version v0.1, on Sun Mar 7 19:25:23 2021 GMT
1) h^ -5 q^ -9 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-6 δ|^0
2) h^ -4 q^ -7 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-4 δ|^0
3) h^-10 q^-17 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-14 δ|^1
4) h^ -9 q^-15 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-12 δ|^1
5) h^ -5 q^ -9 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^-24/5 δ|^0
6) h^ -3 q^ -7 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^-1
7) h^ -2 q^ -5 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^-1
8) h^ -6 q^-11 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^0
options -c11-qs
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxKhr-c11-qs', generated by kht, version v0.1, on Sun Mar 7 19:25:23 2021 GMT
1) h^ -5 q^ -9 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-6 δ|^0
2) h^ -4 q^ -7 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-4 δ|^0
3) h^-10 q^-17 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-14 δ|^1
4) h^ -9 q^-15 δ^ 3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s1(0) q^-12 δ|^1
5) h^ -5 q^ -9 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^-24/5 δ|^0
6) h^ -3 q^ -7 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^-1
7) h^ -2 q^ -5 δ^-1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^-1
8) h^ -6 q^-11 δ^ 1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-6 δ|^0
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c2
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxCKh-c2', generated by kht, version v0.1, on Sun Mar 7 18:15:16 2021 GMT
1) h^ 0 q^ -2 δ^-1 ⬮
2) h^-6 q^-14 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^-3 q^ -8 δ^-1 ⬮——H—>⬮
7) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
8) h^-1 q^ -4 δ^-1 ⬮——H—>⬮
options -c3
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxCKh-c3', generated by kht, version v0.1, on Sun Mar 7 18:15:16 2021 GMT
1) h^ 0 q^ -2 δ^-1 ⬮
2) h^-6 q^-14 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^-3 q^ -8 δ^-1 ⬮——H—>⬮
7) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
8) h^-1 q^ -4 δ^-1 ⬮——H—>⬮
options -c5
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxCKh-c5', generated by kht, version v0.1, on Sun Mar 7 18:15:16 2021 GMT
1) h^ 0 q^ -2 δ^-1 ⬮
2) h^-6 q^-14 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^-3 q^ -8 δ^-1 ⬮——H—>⬮
7) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
8) h^-1 q^ -4 δ^-1 ⬮——H—>⬮
options -c7
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxCKh-c7', generated by kht, version v0.1, on Sun Mar 7 18:15:16 2021 GMT
1) h^ 0 q^ -2 δ^-1 ⬮
2) h^-6 q^-14 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^-3 q^ -8 δ^-1 ⬮——H—>⬮
7) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
8) h^-1 q^ -4 δ^-1 ⬮——H—>⬮
options -c11
(diagram)
(metadata)
% file 'examples/strong_inversions/8_21-2/cxCKh-c11', generated by kht, version v0.1, on Sun Mar 7 18:15:16 2021 GMT
1) h^ 0 q^ -2 δ^-1 ⬮
2) h^-6 q^-14 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^-3 q^ -8 δ^-1 ⬮——H—>⬮
7) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
8) h^-1 q^ -4 δ^-1 ⬮——H—>⬮