Year: 2026
Type: preprint
Abstract: We study near alternating sign matrices with prescribed row and column weights. After recalling the basic definitions and the necessary conditions coming from the Gale--Ryser theorem, we give a graph-theoretic characterization of the existence problem. More precisely, we show that a near alternating sign matrix with prescribed row and column weight sequences exists if and only if there exists a binary array with the same weights whose associated adjacency graph is bipartite. This reformulation shows that the Gale--Ryser conditions are not sufficient in general. We then formulate a natural conjecture up to permutations of the row and column weight sequences, and present some positive results, based on convex binary arrays and composition constructions.
Source: arXiv (Cornell University)
Author: Traetta, Tommaso
Institution: University of Brescia
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212028822