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intersecting families of permutations: erdős–ko–rado theorem

Proceedings of the Edinburgh Mathematical Society (1)

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Intersecting families in classical Coxeter groups
Part of
- Algebraic combinatorics
- Representation theory of groups
Li Wang
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 56 / Issue 3 / October 2013

Published online by Cambridge University Press:

28 June 2013, pp. 887-908
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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.