Geodesic
An extension of the Erdős-Ko-Rado theorem to uniform set partitions
Ars Mathematica Contemporanea, Tome 23 (2023) no. 4, article no. 02, 21 p.

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A (k,ℓ)-partition is a set partition which has ℓ blocks each of size k. Two uniform set partitions P and Q are said to be partially t-intersecting if there exist blocks Pi in P and Qj in Q such that |Pi∩Qj| ≥ t. In this paper we prove a version of the Erdős-Ko-Rado theorem for partially 2-intersecting (k,ℓ)-partitions. In particular, we show for ℓ sufficiently large, the set of all (k,ℓ)-partitions in which a block contains a fixed pair is the largest set of 2-partially intersecting (k,ℓ)-partitions. For for k = 3, we show this result holds for all ℓ.
DOI : 10.26493/1855-3974.2698.6fe
Keywords: Erdos-Ko-Rado Theorem, Uniform set partitions, Ratio bound, Cliques, Cocliques, Quotient graphs 
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Karen Meagher; Mahsa N. Shirazi; Brett Stevens. An extension of the Erdős-Ko-Rado theorem to uniform set partitions. Ars Mathematica Contemporanea, Tome 23 (2023) no. 4, article  no. 02, 21 p. doi : 10.26493/1855-3974.2698.6fe. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2698.6fe/

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