12 papers · 1 filter
Complex generalised weighing matrices in centraliser algebras of monomial representations
Ronan Egan, Padraig Ó Catháin, Andrea Švob
An matrix with exactly non-zero entries taken from the set of complex roots of unity in each row and column satisfying is a com…
Cliques in graphs constructed from Strongly Orthogonal Subsets in exceptional root systems
Patrick J. Browne, Pádraig Ó Catháin
Given a root system , two roots are said to be \emph{strongly orthogonal} if neither their sum nor difference is a root. Gashi defined a family of graphs with vertices labelled…
Symmetries of regular -graphs
Daniel R Hawtin, Padraig Ó Catháin
Given a finite vector space , the -analogue of a graph, called a -graph, is a pair , where is the set of -dime…
Extendibility of Latin Hypercuboids
Candida Bowtell, Alice Devillers, André Kündgen +2
A Latin hypercuboid of order is a -dimensional matrix of dimensions , with symbols from a set of cardinality such that each symbol…
A generalisation of bent vectors for Butson Hadamard matrices
José Andrés Armario, Ronan Egan, Hadi Kharaghani +1
An complex matrix with entries in the roots of unity which satisfies is called a Butson Hadamard matrix. While a matrix with…
Centraliser algebras of monomial representations and applications in combinatorics
Santiago Barrera Acevedo, Padraig Ó Catháin, Heiko Dietrich +1
Centraliser algebras of monomial representations of finite groups may be constructed and studied using methods similar to those employed in the study of permutation groups. Guided…