Tesler matrices and Lusztig data

TL;DR

This paper explores the asymptotic behavior of Tesler matrices through Kostant pictures, revealing new partial order relationships and deriving logarithmic asymptotics for certain matrix families.

Contribution

It establishes a refined partial order on Kostant pictures and connects it to Tesler matrices, providing new insights into their asymptotic properties.

Findings

Lusztig data partial order refines the merge order on Kostant pictures.

Merge order on Kostant pictures is equivalent to a partial order on Tesler matrices.

Logarithmic asymptotics are derived for specific Tesler matrix families.

Abstract

We study asymptotics of Tesler matrices using Kostant pictures, as well as partial orders on these. We show that the Lusztig data partial order on Kostant pictures refines the 'merge' partial order on Kostant pictures, and that the merge partial order on Kostant pictures is equivalent to a partial order on Tesler matrices. This equivalence requires integral flow graphs. Using Kostant pictures we find logarithmic asymptotics of some families of Tesler matrices.