2021/05/14 by Klaus Metsch, Metsch, Klaus · 1 citation
Engineering · Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2105.06764
openalex publication_date 2021/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A flag of a finite set S is a set f of non-empty proper subsets of S such that A⊆ B or B⊆ A for all A,B∈ f. The set \|A|:A∈ f\ is called the type of f. Two flags f and f' are in general position (with respect to S) when A∩ B=∅ or A∪ B=S for all A∈ f and B∈ f'. We study sets of flags of a fixed type T that are mutually not in general position and are interested in the largest cardinality of these sets. This is a generalization of the classical Erdös-Ko-Rado problem. We will give some basic facts and determine the largest cardinality in several non-trivial cases. For this we will define graphs whose vertices are flags and the problem is to determine the independence number of these graphs.