Root polytopes, parking functions, and the HOMFLY polynomial

Tamás Kálmán; Hitoshi Murakami

doi:10.4171/QT/89

Root polytopes, parking functions, and the HOMFLY polynomial

Tamás Kálmán, Hitoshi Murakami

INF - Computer and Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 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 language	English
Pages (from-to)	205-248
Number of pages	44
Journal	Quantum Topology
Volume	8
Issue number	2
DOIs	https://doi.org/10.4171/QT/89
Publication status	Published - 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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10.4171/QT/89

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title = "Root polytopes, parking functions, and the HOMFLY polynomial",

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.",

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T1 - Root polytopes, parking functions, and the HOMFLY polynomial

AU - Kálmán, Tamás

AU - Murakami, Hitoshi

N1 - Publisher Copyright: © European Mathematical Society.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Alternating link

KW - H-vector

KW - HOMFLY polynomial

KW - Parking function

KW - Root polytope

KW - Seifert graph

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EP - 248

JO - Quantum Topology

JF - Quantum Topology

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ER -

Root polytopes, parking functions, and the HOMFLY polynomial

Abstract

Keywords

ASJC Scopus subject areas

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