3 papers
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…
math.RA2024
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…
math.GR2013
Unitary groups over local rings
J. Cruickshank, A. Herman, R. Quinlan +1
Structural properties of unitary groups over local, not necessarily commutative, rings are developed, with applications to the computation of the orders of these groups (when finit…