Interior polynomial for signed bipartite graphs and the HOMFLY polynomial

2017/05/15 by Keiju Kato, Kato, Keiju · 1 citation
Mathematics · #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1705.05063

Abstract

The interior polynomial is an invariant of bipartite graphs, and a part of the HOMFLY polynomial of a special alternating link coincides with the interior polynomial of the Seifert graph of the link. We extend the interior polynomial to signed bipartite graphs, and we show that, in the planar case, it is equal to a part of the HOMFLY polynomial of a naturally associated link. We also establish some other, more basic properties of this new notion. This leads to new identities involving the original interior polynomial.

Cited by

• A mirroring formula for the interior polynomial of a bipartite graph

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