3 papers
math.CO2024
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}…
math.CO2023
Invariants of Quadratic Forms and applications in Design Theory
Oliver W. Gnilke, Padraig O Cathain, Oktay Olmez +1
The study of regular incidence structures such as projective planes and symmetric block designs is a well established topic in discrete mathematics. Work of Bruck, Ryser and Chowla…
math.CO2023
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…