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arXiv · 2207.05947

On the EKR Module property

Cai Heng Li·Venkata Raghu Tej
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Abstract

In the recent years, the generalization of the Erd\H{o}s-Ko-Rado (EKR) theorem to permutation groups has been of much interest. A transitive group is said to satisfy the EKR-module property if the characteristic vector of every maximum intersecting set is a linear combination of the characteristic vectors of cosets of stabilizers of points. This generalization of the well-know permutation group version of the Erd\H{o}s-Ko-Rado (EKR) theorem, was introduced by K. Meagher. In this article, we present several infinite families of permutation groups satisfying the EKR-module property, which shows that permutation groups satisfying this property are quite diverse.

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Cai Heng Li, Venkata Raghu Tej. 2022-07-13. On the EKR Module property. https://arxiv.org/abs/2207.05947

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