The set of alternating sign matrices which are determined by their X-ray is a member of the Catalan family

TL;DR

This paper establishes a bijection between Dyck paths and a special class of alternating sign matrices characterized by their antidiagonal sums, linking combinatorial structures to the Catalan family.

Contribution

It introduces a novel bijection connecting Dyck paths with a subset of alternating sign matrices defined by their X-ray properties.

Findings

Identifies a bijection between Dyck paths and certain alternating sign matrices.

Shows these matrices are part of the Catalan family.

Provides a new combinatorial interpretation of these matrices.

Abstract

We exhibit a bijection between Dyck paths and alternating sign matrices which are determined by their antidiagonal sums.