Root polytopes, parking functions, and the HOMFLY polynomial

  • Tamás Kálmán

    Tokyo Institute of Technology, Japan
  • Hitoshi Murakami

    Tohoku University, Sendai, Japan

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 -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 -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.

Cite this article

Tamás Kálmán, Hitoshi Murakami, Root polytopes, parking functions, and the HOMFLY polynomial. Quantum Topol. 8 (2017), no. 2, pp. 205–248

DOI 10.4171/QT/89