Abstract
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.
Citation
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
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