Journal article

Publication year: 2022

Journal: Journal of Combinatorial Theory, Series A

Volume number: 191

ISSN: 0097-3165

eISSN: 1096-0899

Open access status: Green

DOI Link: https://doi.org/10.1016/j.jcta.2022.105641

Publisher: Elsevier

Abstract: 
A flag of a finite set S is a set f of non-empty proper subsets of S such that A subset of B or B subset of A for all A, B is an element of f. The set {|A| : A is an element of f} is called the type of f. Two flags f and f' are in general position (with respect to S) when A n B = theta or A U B = S for all A is an element of f and B is an element of 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 Erdos-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. (C) 2022 Elsevier Inc. All rights reserved.

Harvard Citation style: Metsch, K. (2022) Erdos-Ko-Rado sets of flags of finite sets, Journal of Combinatorial Theory, Series A, 191, Article 105641. https://doi.org/10.1016/j.jcta.2022.105641

APA Citation style: Metsch, K. (2022). Erdos-Ko-Rado sets of flags of finite sets. Journal of Combinatorial Theory, Series A. 191, Article 105641. https://doi.org/10.1016/j.jcta.2022.105641