A combinatorial model for the transition matrix between the Specht and web bases

TL;DR

This paper introduces web permutations to interpret the transition matrix between Specht and web bases, addressing Rhoades's question and exploring their enumerative properties.

Contribution

It provides a novel combinatorial model for the transition matrix between Specht and web bases using web permutations.

Findings

Combinatorial interpretation of matrix entries

Introduction of web permutations

Enumeration of web permutations

Abstract

We introduce a new class of permutations, called web permutations. Using these permutations, we provide a combinatorial interpretation for entries of the transition matrix between the Specht and web bases, which answers Rhoades's question. Furthermore, we study enumerative properties of these permutations.