Top-degree HOMFLY conjecture for arbitrary plabic graphs

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Let GG be a plabic graph with c⁡(G)\operatorname{c}(G) connected components and nn interior faces. Let LGplab⁡L^{\operatorname{plab}}_G be its associated plabic graph link, and let \PtopL(q)\Ptop_L(q) be obtained from the top aa-degree term of its HOMFLY polynomial by the stated specialization. Top-degree HOMFLY conjecture.

deg⁡atop⁡P(LGplab⁡)=c⁡(G)−n−1,\deg_a^{\operatorname{top}}P(L^{\operatorname{plab}}_G)=\operatorname{c}(G)-n-1, deg⁡(\PtopL(q))=n,\deg(\Ptop_L(q))=n,

and the leading coefficient of \PtopL(q)\Ptop_L(q) is 11. This is presented as a basic extension beyond simple plabic graphs, including graphs with interior leaves. The supplied source gives no resolution status.

References

Primary source

Pavel Galashin and Thomas Lam, “Plabic links, quivers, and skein relations”, arXiv:2208.01175 (2022).

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