A generalization of Alternating Sign Matrices
Richard A. Brualdi, Hwa Kyung Kim
TL;DR
This paper generalizes the concept of alternating sign matrices by allowing the first and last nonzero entries in each row and column to be either +1 or -1, and establishes conditions for their existence.
Contribution
It introduces a broader class of matrices with specified boundary signs and characterizes the conditions for their existence.
Findings
Derived necessary and sufficient conditions for the existence of generalized matrices.
Extended the theory of alternating sign matrices to include variable boundary signs.
Provided a framework for constructing such matrices under given conditions.
Abstract
In alternating sign matrices the first and last nonzero entry in each row and column is specified to be +1. Such matrices always exist. We investigate a generalization by specifying independently the sign of the first and last nonzero entry in each row and column to be either a +1 or a -1. We determine necessary and sufficient conditions for such matrices to exist.
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