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arXiv · 2609.07118

A note on near alternating sign matrices with prescribed row and column weights

Tommaso Traetta
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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.

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Tommaso Traetta. 2026-09-07. A note on near alternating sign matrices with prescribed row and column weights. https://arxiv.org/abs/2609.07118

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