4 papers
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…
A Bollobás-type problem: from root systems to Erdős-Ko-Rado
Patrick J. Browne, Qëndrim R. Gashi, Padraig Ó Catháin
Motivated by an Erdős--Ko--Rado type problem on sets of strongly orthogonal roots in the root system, we estimate bounds for the size of a family of pairs $(A_{i}, B_{i}…
Segre's theorem on ovals in Desarguesian projective planes
Patrick J. Browne, Steven T. Dougherty, Padraig Ó Catháin
Segre's theorem on ovals in projective spaces is an ingenious result from the mid-twentieth century which requires surprisingly little background to prove. This note, suitable for…
A Survey of the Hadamard Maximal Determinant Problem
Patrick Browne, Ronan Egan, Fintan Hegarty +1
In a celebrated paper of 1893, Hadamard established the maximal determinant theorem, which establishes an upper bound on the determinant of a matrix with complex entries of norm at…