Root polytopes, parking functions, and the HOMFLY polynomial

Tamás Kálmán, Hitoshi Murakami

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We show that for a special alternating link diagram, the following three polynomials are essentially the same: a) the part of the HOMFLY polynomial that corresponds to the leading term in the Alexander polynomial; b) the h-vector for a triangulation of the root polytope of the Seifert graph and c) the enumerator of parking functions for the planar dual of the Seifert graph. These observations yield formulas for the maximal z-degree part of the HOMFLY polynomial of an arbitrary homogeneous link as well. Our result is part of a program aimed at reading HOMFLY coefficients out of Floer homology.

Original languageEnglish
Pages (from-to)205-248
Number of pages44
JournalQuantum Topology
Volume8
Issue number2
DOIs
Publication statusPublished - 2017

Keywords

  • Alternating link
  • H-vector
  • HOMFLY polynomial
  • Parking function
  • Root polytope
  • Seifert graph

ASJC Scopus subject areas

  • Mathematical Physics
  • Geometry and Topology

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