Smith Normal Form of Matrices Associated with Differential Posets

TL;DR

This paper proves a conjecture regarding the existence of Smith normal form for certain operators associated with differential posets, advancing understanding in algebraic combinatorics.

Contribution

It establishes the Smith normal form for $DU$-operators in a specific class of $r$-differential posets, confirming a conjecture by Miller and Reiner.

Findings

Smith normal form exists for $DU$-operators in the studied differential posets

Confirms Miller and Reiner's conjecture for a class of $r$-differential posets

Enhances algebraic understanding of differential poset operators

Abstract

We prove a conjecture of Miller and Reiner on the existence of Smith normal form for the $DU$-operators for a certain class of $r$-differential posets.