On Schur function expansions of Thom polynomials

TL;DR

This paper explores the computation of Thom polynomials for singularity classes using Schur function expansions, reviewing known bounds, recursions, and providing new and existing calculations for specific singularities.

Contribution

It introduces new recursive methods and computations for Thom polynomials in the Schur function basis, expanding understanding of their structure and bounds.

Findings

Bounds on partition length and rectangle containment established

Recursion formulas for coefficients derived

New computations of Thom polynomials for certain singularities provided

Abstract

We discuss computations of the Thom polynomials of singularity classes of maps in the basis of Schur functions. We survey the known results about the bound on the length and a rectangle containment for partitions appearing in such Schur function expansions. We describe several recursions for the coefficients. For some singularities, we give old and new computations of their Thom polynomials.