Involve: A Journal of Mathematics

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  • Volume 8, Number 1 (2015), 119-127.

An Erdős–Ko–Rado theorem for subset partitions

Adam Dyck and Karen Meagher

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A k-subset partition, or (k,)-subpartition, is a k-subset of an n-set that is partitioned into distinct blocks, each of size k. Two (k,)-subpartitions are said to t-intersect if they have at least t blocks in common. In this paper, we prove an Erdős–Ko–Rado theorem for intersecting families of (k,)-subpartitions. We show that for n k, 2 and k 3, the number of (k,)-subpartitions in the largest 1-intersecting family is at most nk k n2k k n(1)k k ( 1)!, and that this bound is only attained by the family of (k,)-subpartitions with a common fixed block, known as the canonical intersecting family of (k,)-subpartitions. Further, provided that n is sufficiently large relative to k, and t, the largest t-intersecting family is the family of (k,)-subpartitions that contain a common set of t fixed blocks.

Article information

Involve, Volume 8, Number 1 (2015), 119-127.

Received: 3 October 2013
Revised: 9 April 2014
Accepted: 12 April 2014
First available in Project Euclid: 22 November 2017

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Zentralblatt MATH identifier

Primary: 05D05: Extremal set theory

Erdős–Ko–Rado theorem set partitions


Dyck, Adam; Meagher, Karen. An Erdős–Ko–Rado theorem for subset partitions. Involve 8 (2015), no. 1, 119--127. doi:10.2140/involve.2015.8.119.

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