4 papers
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…
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…
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…
Groups of singular alternating sign matrices
Cian O'Brien, Rachel Quinlan
We investigate multiplicative groups consisting entirely of singular alternating sign matrices (ASMs), and present several constructions of such groups. It is shown that every fini…