3 papers
math.CO2021
Alternating sign matrices of finite multiplicative order
Cian O'Brien, Rachel Quinlan
We investigate alternating sign matrices that are not permutation matrices, but have finite order in a general linear group. We classify all such examples of the form , where…
math.CO2020
Alternating Sign Hypermatrix Decompositions of Latin-like Squares
Cian O'Brien
To any Latin square , we may associate a unique sequence of mutually orthogonal permutation matrices such that . Brua…
math.CO2019
Alternating Signed Bipartite Graphs and Difference-1 Colourings
Cian O'Brien, Kevin Jennings, Rachel Quinlan
We investigate a class of 2-edge coloured bipartite graphs known as alternating signed bipartite graphs (ASBGs) that encode the information in alternating sign matrices. The centra…