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math.CO2026
Generalising Latin square orthogonality and Frobenius-König with alternating sign matrices
Alena Ernst, Stefano Lia, Cian O'Brien +2
The theory of Latin squares has a long history. While the objects themselves appeared earlier, the study of their general mathematical theory dates back to Euler in the 18th centur…
math.CO2026
A Bruhat order for Latin squares and alternating sign hypermatrices
Angela Carnevale, Cian O'Brien
The Bruhat order on permutation matrices extends to alternating sign matrices via corner-sum matrices, where the order is given by entrywise domination. A classical result of Lasco…
math.CO2025
The rank distribution of matrices representing graphs with a long induced path over the field of two elements
Badriah Safarji, Cian O'Brien, Rachel Quinlan
A square matrix represents a graph if its nonzero off-diagonal entries encode the adjacencies of , subject to a fixed ordering of the vertices. Over the field of two ele…