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2015 An Erdős–Ko–Rado theorem for subset partitions
Adam Dyck, Karen Meagher
Involve 8(1): 119-127 (2015). DOI: 10.2140/involve.2015.8.119

Abstract

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.

Citation

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Adam Dyck. Karen Meagher. "An Erdős–Ko–Rado theorem for subset partitions." Involve 8 (1) 119 - 127, 2015. https://doi.org/10.2140/involve.2015.8.119

Information

Received: 3 October 2013; Revised: 9 April 2014; Accepted: 12 April 2014; Published: 2015
First available in Project Euclid: 22 November 2017

zbMATH: 1309.05176
MathSciNet: MR3321715
Digital Object Identifier: 10.2140/involve.2015.8.119

Subjects:
Primary: 05D05

Keywords: Erdős–Ko–Rado theorem , set partitions

Rights: Copyright © 2015 Mathematical Sciences Publishers

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