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Input data and context
% 9_2-1
s.l1.y0.y0.y0.y0.y0.y0.y0.y0.y1.u2
,1
% Symmetry 1 of a 2-bridge knot corresponding to the fraction 15/2 = [8,-2] (Sakuma, Prop. 3.6, symmetry 1).
% Simplifies with options '-qs' to r1.x2.y1.y1.y1.r2.x3.y2.y1.y2.y1.y2.y1.y1.y1.y2.y1.y2.y1.y1.y1.y2.y2.y1.y2.y1.y2.y1.y1.y1.y1.y2.y1.y2.y2.y2.y1.y1.y2.x3.y1.y1.y1.x2.u1.y1.y1.y1.x0.y2.u1.y0.y0.y0
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_2-1/cxBNr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^46 δ^23 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_2-1/cxBNr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^46 δ^23 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_2-1/cxBNr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^46 δ^23 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_2-1/cxBNr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^46 δ^23 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_2-1/cxBNr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^0 q^46 δ^23 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯~>⬮—>⬮~>⬮—>⬮
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_2-1/cxKhr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^27 q^87 δ^33/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^456/5 δ|^16
2) h^23 q^81 δ^35/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^86 δ|^17
3) h^19 q^75 δ^37/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^80 δ|^18
4) h^15 q^69 δ^39/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^74 δ|^19
5) h^11 q^63 δ^41/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^68 δ|^20
6) h^ 7 q^57 δ^43/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^62 δ|^21
7) h^ 3 q^51 δ^45/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^56 δ|^22
8) h^-1 q^45 δ^47/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^50 δ|^23
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_2-1/cxKhr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^27 q^87 δ^33/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^456/5 δ|^16
2) h^23 q^81 δ^35/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^86 δ|^17
3) h^19 q^75 δ^37/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^80 δ|^18
4) h^15 q^69 δ^39/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^74 δ|^19
5) h^11 q^63 δ^41/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^68 δ|^20
6) h^ 7 q^57 δ^43/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^62 δ|^21
7) h^ 3 q^51 δ^45/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^56 δ|^22
8) h^-1 q^45 δ^47/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^50 δ|^23
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_2-1/cxKhr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^27 q^87 δ^33/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^456/5 δ|^16
2) h^23 q^81 δ^35/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^86 δ|^17
3) h^19 q^75 δ^37/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^80 δ|^18
4) h^15 q^69 δ^39/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^74 δ|^19
5) h^11 q^63 δ^41/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^68 δ|^20
6) h^ 7 q^57 δ^43/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^62 δ|^21
7) h^ 3 q^51 δ^45/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^56 δ|^22
8) h^-1 q^45 δ^47/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^50 δ|^23
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_2-1/cxKhr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^27 q^87 δ^33/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^456/5 δ|^16
2) h^23 q^81 δ^35/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^86 δ|^17
3) h^19 q^75 δ^37/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^80 δ|^18
4) h^15 q^69 δ^39/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^74 δ|^19
5) h^11 q^63 δ^41/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^68 δ|^20
6) h^ 7 q^57 δ^43/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^62 δ|^21
7) h^ 3 q^51 δ^45/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^56 δ|^22
8) h^-1 q^45 δ^47/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^50 δ|^23
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_2-1/cxKhr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^27 q^87 δ^33/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬯<— r(1/4) q^456/5 δ|^16
2) h^23 q^81 δ^35/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^86 δ|^17
3) h^19 q^75 δ^37/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^80 δ|^18
4) h^15 q^69 δ^39/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^74 δ|^19
5) h^11 q^63 δ^41/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^68 δ|^20
6) h^ 7 q^57 δ^43/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^62 δ|^21
7) h^ 3 q^51 δ^45/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^56 δ|^22
8) h^-1 q^45 δ^47/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^50 δ|^23
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c0
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_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^-9 q^-20 δ^-1 ⬮——H—>⬮
3) h^-7 q^-16 δ^-1 ⬮——H—>⬮
4) h^-6 q^-14 δ^-1 ⬮——H—>⬮
5) h^-5 q^-12 δ^-1 ⬮——H—>⬮
6) h^-4 q^-10 δ^-1 ⬮——H—>⬮
7) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
8) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c2
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_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^-9 q^-20 δ^-1 ⬮——H—>⬮
3) h^-7 q^-16 δ^-1 ⬮——H—>⬮
4) h^-6 q^-14 δ^-1 ⬮——H—>⬮
5) h^-5 q^-12 δ^-1 ⬮——H—>⬮
6) h^-4 q^-10 δ^-1 ⬮——H—>⬮
7) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
8) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c3
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_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^-9 q^-20 δ^-1 ⬮——H—>⬮
3) h^-7 q^-16 δ^-1 ⬮——H—>⬮
4) h^-6 q^-14 δ^-1 ⬮——H—>⬮
5) h^-5 q^-12 δ^-1 ⬮——H—>⬮
6) h^-4 q^-10 δ^-1 ⬮——H—>⬮
7) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
8) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c5
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_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^-9 q^-20 δ^-1 ⬮——H—>⬮
3) h^-7 q^-16 δ^-1 ⬮——H—>⬮
4) h^-6 q^-14 δ^-1 ⬮——H—>⬮
5) h^-5 q^-12 δ^-1 ⬮——H—>⬮
6) h^-4 q^-10 δ^-1 ⬮——H—>⬮
7) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
8) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c7
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_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^-9 q^-20 δ^-1 ⬮——H—>⬮
3) h^-7 q^-16 δ^-1 ⬮——H—>⬮
4) h^-6 q^-14 δ^-1 ⬮——H—>⬮
5) h^-5 q^-12 δ^-1 ⬮——H—>⬮
6) h^-4 q^-10 δ^-1 ⬮——H—>⬮
7) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
8) h^-2 q^ -6 δ^-1 ⬮——H—>⬮
options -c11
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_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^-9 q^-20 δ^-1 ⬮——H—>⬮
3) h^-7 q^-16 δ^-1 ⬮——H—>⬮
4) h^-6 q^-14 δ^-1 ⬮——H—>⬮
5) h^-5 q^-12 δ^-1 ⬮——H—>⬮
6) h^-4 q^-10 δ^-1 ⬮——H—>⬮
7) h^-3 q^ -8 δ^-1 ⬮——H—>⬮
8) h^-2 q^ -6 δ^-1 ⬮——H—>⬮