Total positivity of a class of combinatorial matrices

TL;DR

This paper proves the total positivity of a class of combinatorial matrices constructed from sequences related to symmetric functions, using combinatorial and algebraic techniques.

Contribution

It introduces a new class of matrices based on symmetric functions and establishes their total positivity through combinatorial methods.

Findings

Matrices are totally positive.

Uses Lindström-Gessel-Viennot Lemma for proof.

Connects combinatorial sequences with algebraic positivity.

Abstract

In this paper, we consider matrices whose entries are combinatorial sequences which can be expressed in terms of a convolution of elementary and complete homogeneous symmetric functions. We establish the total positivity of these matrices using the Lindstr\"om-Gessel-Viennot Lemma.