# Toeplitz minors and specializations of skew Schur polynomials

## TL;DR

This paper links Toeplitz matrix minors to symmetric functions, deriving explicit formulas for a Selberg-Morris integral and skew Schur polynomial specializations, advancing understanding of their algebraic and combinatorial properties.

## Contribution

It provides explicit formulas connecting Toeplitz minors with symmetric functions, including new results for Selberg-Morris integrals and skew Schur polynomial specializations.

## Key findings

- Explicit formulas for Toeplitz minors in terms of symmetric functions
- New expressions for Selberg-Morris integrals
- Specializations of skew Schur polynomials derived from Toeplitz matrices

## Abstract

We express minors of Toeplitz matrices of finite and large dimension in terms of symmetric functions. Comparing the resulting expressions with the inverses of some Toeplitz matrices, we obtain explicit formulas for a Selberg-Morris integral and for specializations of certain skew Schur polynomials.