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Intersecting families in classical Coxeter groups

Part of: Algebraic combinatorics Representation theory of groups

Published online by Cambridge University Press:  28 June 2013

Li Wang
Li Wang*
Affiliation:
Department of Mathematics, Shanghai Normal University, Guilin Road 100, Shanghai 200234, People's Republic of China (wlmath@shnu.edu.cn)
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Abstract

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Let Ω be a finite set and let G be a permutation group acting on it. A subset H of G is called t-intersecting if any two elements in H agree on at least t points. Let SDn and SBn be the classical Coxeter group of type Dn and type Bn, respectively. We show that the maximum-sized (2t)-intersecting families in SDn and SBn are precisely cosets of stabilizers of t points in [n] ≔ {1, 2, …, n}, provided n is sufficiently large depending on t.

Keywords

intersecting families of permutations: Erdős–Ko–Rado theoremrepresentation theoryclassical coxeter groups

MSC classification

Secondary: 05E10: Combinatorial aspects of representation theory 20C15: Ordinary representations and characters
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 3 , October 2013 , pp. 887 - 908
Copyright
Copyright © Edinburgh Mathematical Society 2013 

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