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% 9_1
s.r1.y0.y0.y1.y0.y0.y1.y0.y0.y1.y0.y0.y1.u2
,1
% Symmetry of a 2-bridge knot corresponding to the fraction 9/8 = [2,-2,2,-2,2,-2,2,-2] (Sakuma, Appendix I).
% Simplifies with options '-qs' to r2.l3.x1.y2.y2.y2.y3.y4.x1.y2.y2.x1.x2.x3.x3.x2.x1.y3.y2.x1.u0.y1.y2.y1.u0.y0.y0.y0.y0.y0.y0.y0.y0.y0.y0.y0.y0.y0.y0.y0
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxBNr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-4 q^10 δ^9 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-2 q^14 δ^9 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 0 q^16 δ^8 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxBNr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-4 q^10 δ^9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-2 q^14 δ^9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 0 q^16 δ^8 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxBNr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-4 q^10 δ^9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-2 q^14 δ^9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 0 q^16 δ^8 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxBNr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-4 q^10 δ^9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-2 q^14 δ^9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 0 q^16 δ^8 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxBNr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-4 q^10 δ^9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-2 q^14 δ^9 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 0 q^16 δ^8 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxKhr-c2-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-5 q^ 9 δ^19/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^14 δ|^9
2) h^-4 q^11 δ^19/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^9
3) h^-3 q^13 δ^19/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^9
4) h^-2 q^15 δ^19/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^20 δ|^9
5) h^-1 q^15 δ^17/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/16) q^528/17 δ|^8
options -c3-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxKhr-c3-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-5 q^ 9 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^14 δ|^9
2) h^-4 q^11 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^9
3) h^-3 q^13 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^9
4) h^-2 q^15 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^20 δ|^9
5) h^-1 q^15 δ^17/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/16) q^528/17 δ|^8
options -c5-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxKhr-c5-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-5 q^ 9 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^14 δ|^9
2) h^-4 q^11 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^9
3) h^-3 q^13 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^9
4) h^-2 q^15 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^20 δ|^9
5) h^-1 q^15 δ^17/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/16) q^528/17 δ|^8
options -c7-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxKhr-c7-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-5 q^ 9 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^14 δ|^9
2) h^-4 q^11 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^9
3) h^-3 q^13 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^9
4) h^-2 q^15 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^20 δ|^9
5) h^-1 q^15 δ^17/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/16) q^528/17 δ|^8
options -c11-q
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxKhr-c11-q', generated by kht, version v0.1, on Sun Mar 7 16:05:13 2021 GMT
1) h^-5 q^ 9 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^14 δ|^9
2) h^-4 q^11 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^16 δ|^9
3) h^-3 q^13 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^18 δ|^9
4) h^-2 q^15 δ^19/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^20 δ|^9
5) h^-1 q^15 δ^17/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/16) q^528/17 δ|^8
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c0
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxCKh-c0', generated by kht, version v0.1, on Sun Mar 7 15:45:53 2021 GMT
1) h^ 0 q^ -8 δ^-4 ⬮
2) h^-9 q^-26 δ^-4 ⬮——H—>⬮
3) h^-7 q^-22 δ^-4 ⬮——H—>⬮
4) h^-5 q^-18 δ^-4 ⬮——H—>⬮
5) h^-3 q^-14 δ^-4 ⬮——H—>⬮
options -c2
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxCKh-c2', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ -8 δ^-4 ⬮
2) h^-9 q^-26 δ^-4 ⬮——H—>⬮
3) h^-7 q^-22 δ^-4 ⬮——H—>⬮
4) h^-5 q^-18 δ^-4 ⬮——H—>⬮
5) h^-3 q^-14 δ^-4 ⬮——H—>⬮
options -c3
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxCKh-c3', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ -8 δ^-4 ⬮
2) h^-9 q^-26 δ^-4 ⬮——H—>⬮
3) h^-7 q^-22 δ^-4 ⬮——H—>⬮
4) h^-5 q^-18 δ^-4 ⬮——H—>⬮
5) h^-3 q^-14 δ^-4 ⬮——H—>⬮
options -c5
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxCKh-c5', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ -8 δ^-4 ⬮
2) h^-9 q^-26 δ^-4 ⬮——H—>⬮
3) h^-7 q^-22 δ^-4 ⬮——H—>⬮
4) h^-5 q^-18 δ^-4 ⬮——H—>⬮
5) h^-3 q^-14 δ^-4 ⬮——H—>⬮
options -c7
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxCKh-c7', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ -8 δ^-4 ⬮
2) h^-9 q^-26 δ^-4 ⬮——H—>⬮
3) h^-7 q^-22 δ^-4 ⬮——H—>⬮
4) h^-5 q^-18 δ^-4 ⬮——H—>⬮
5) h^-3 q^-14 δ^-4 ⬮——H—>⬮
options -c11
(diagram)
(metadata)
% file 'examples/strong_inversions/2-bridge_knots/9_1/cxCKh-c11', generated by kht, version v0.1, on Sun Mar 7 15:58:53 2021 GMT
1) h^ 0 q^ -8 δ^-4 ⬮
2) h^-9 q^-26 δ^-4 ⬮——H—>⬮
3) h^-7 q^-22 δ^-4 ⬮——H—>⬮
4) h^-5 q^-18 δ^-4 ⬮——H—>⬮
5) h^-3 q^-14 δ^-4 ⬮——H—>⬮