An algebraic approach to Erdős-Ko-Rado sets of flags in spherical buildings II

2024/08/09 by Jan De Beule, De Beule, Jan, Sam Mattheus +3
Computer Science · Engineering · Mathematics · #05C50 #05E18 #05E30 #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2408.05015

openalex publication_date 2024/08/09 · openalex created_date 2024/09/11 · openalex updated_date 2026/07/28

Abstract

We continue our investigation of Erdős-Ko-Rado (EKR) sets of flags in spherical buildings. In previous work, we used the theory of buildings and Iwahori-Hecke algebras to obtain upper bounds on their size. As the next step towards the classification of the maximal EKR-sets, we describe the eigenspaces for the smallest eigenvalue of the opposition graphs. We determine their multiplicity and provide a combinatorial description of spanning sets of these subspaces, from which a complete description of the maximal Erdős-Ko-Rado sets of flags may potentially be found. This was recently shown to be possible for type A_n, n odd, by Heering, Lansdown, and the last author by making use of the current work.

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