# Weighted counting of inversions on alternating sign matrices

## TL;DR

This paper generalizes a known inversion counting formula from permutations to alternating sign matrices, using a sequential construction approach.

## Contribution

It introduces a new weighted counting formula for inversions on alternating sign matrices, extending previous permutation results.

## Key findings

- Extended inversion counting formula to alternating sign matrices
- Utilized sequential construction method for proof
- Builds on recent independent work by Brualdi-Schroeder and the author

## Abstract

We extend the author's formula (2011) of weighted counting of inversions on permutations to the one on alternating sign matrices. The proof is based on the sequential construction of alternating sign matrices from the unit matrix recently shown by Brualdi-Schroeder and the author (both 2017) independently.