Browsing Department of Mathematics and Computer Studies by Subject "Alternating sign matrix"

Now showing items 1-5 of 5

    • Alternating sign hypermatrix decompositions of Latin-like squares 

      O'Brien, Cian (Elsevier, 2020-08-14)
      To any n × n Latin square L, we may associate a unique sequence of mutually orthogonal permutation matrices P = P_1, P_2, ..., P_n such that L = L(P ) = ∑ k_Pk . Brualdi and Dahl (2018) described a generalisation of a ...

    • Alternating sign matrices of finite multiplicative order 

      O'Brien, Cian; Quinlan, Rachel (Elsevier, 2022-07-08)
      We investigate alternating sign matrices that are not permuta- tion matrices, but have finite order in a general linear group. We classify all such examples of the form P + T , where P is a permutation matrix and T has ...

    • Alternating signed bipartite graphs and difference-1 colourings 

      O'Brien, Cian; Jennings, Kevin; Quinlan, Rachel (Elsevier, 2020-07-13)
      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 central question is when a given bipartite ...

    • Groups of singular alternating sign matrices 

      O'Brien, Cian; Quinlan, Rachel (International Linear Algebra Society, 2025-05-20)
      We investigate multiplicative groups consisting entirely of singular alternating sign matrices (ASMs) and present several constructions of such groups. It is shown that every finite group is isomorphic to a group of ...

    • Weighted projections of alternating sign matrices: Latin-like squares and the ASM polytope 

      O'Brien, Cian (Electronic Journal of Combinatorics, 2024-01-12)
      The weighted projection of an alternating sign matrix (ASM) was introduced by Brualdi and Dahl (2018) as a step towards characterising a generalisation of Latin squares they defined using alternating sign hypermatrices. ...