Involve: A Journal of Mathematics
- Volume 8, Number 1 (2015), 119-127.
An Erdős–Ko–Rado theorem for subset partitions
A -subset partition, or -subpartition, is a -subset of an -set that is partitioned into distinct blocks, each of size . Two -subpartitions are said to -intersect if they have at least blocks in common. In this paper, we prove an Erdős–Ko–Rado theorem for intersecting families of -subpartitions. We show that for , and , the number of -subpartitions in the largest -intersecting family is at most , and that this bound is only attained by the family of -subpartitions with a common fixed block, known as the canonical intersecting family of -subpartitions. Further, provided that is sufficiently large relative to and , the largest -intersecting family is the family of -subpartitions that contain a common set of fixed blocks.
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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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 05D05: Extremal set theory
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. https://projecteuclid.org/euclid.involve/1511370844