A (k,\ell)-partition is a set partition which has \ell blocks each of size k. Two uniform set partitions P and Q are said to be partially t-intersecting if there exist blocks P_{i} in P and Q_{j} in Q such that \left| P_{i} \cap Q_{j} \right|\geq t.
Aug 17, 2021
Oct 22, 2024 · 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 ...
In this paper we prove a version of the Erdős-Ko-Rado theorem for partially $2$-intersecting $(k,\ell)$-partitions. In particular, we show for $\ell$ ...
In this paper we prove an extension of the famous Erdős-Ko-Rado (EKR) theorem to set-wise 2-intersecting families of perfect matching on all values of k.
Sep 12, 2024 · In this paper we prove a version of the Erd\H{o}s-Ko-Rado theorem for partially 2-intersecting ( k , ℓ ) (k,\ell) -partitions. In particular, we ...
An extension of the Erdős-Ko-Rado theorem to set-wise 2-intersecting families of perfect matchings · M. N. Shirazi · Published in Discrete Mathematics 5 October ...
The focus of this thesis is on extensions of the EKR theorem to perfect matchings and uniform set partitions.
In mathematics, the Erdős–Ko–Rado theorem limits the number of sets in a family of sets for which every two sets have at least one element in common.
This paper contains a number of results concerning the distribution of sizes of sets in such a family, and also in families where the restriction |A|<n/2 is ...
Aug 1, 2023 · In this paper we prove an extension of the famous Erdős-Ko-Rado (EKR) theorem to set-wise 2-intersecting families of perfect matching on all ...