Erdős-Ko-Rado theorems for uniform set-partition systems
The electronic journal of combinatorics, Tome 12 (2005)
Voir la notice de l'article provenant de la source The Electronic Journal of Combinatorics website
Zbl EuDML
Two set partitions of an $n$-set are said to $t$-intersect if they have $t$ classes in common. A $k$-partition is a set partition with $k$ classes and a $k$-partition is said to be uniform if every class has the same cardinality $c=n/k$. In this paper, we prove a higher order generalization of the Erdős-Ko-Rado theorem for systems of pairwise $t$-intersecting uniform $k$-partitions of an $n$-set. We prove that for $n$ large enough, any such system contains at most $${1\over(k-t)!} {n-tc \choose c} {n-(t+1)c \choose c} \cdots {n-(k-1)c \choose c}$$ partitions and this bound is only attained by a trivially $t$-intersecting system. We also prove that for $t=1$, the result is valid for all $n$. We conclude with some conjectures on this and other types of intersecting partition systems.
Karen Meagher; Lucia Moura. Erdős-Ko-Rado theorems for uniform set-partition systems. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1937
@article{10_37236_1937,
author = {Karen Meagher and Lucia Moura},
title = {Erd\H{o}s-Ko-Rado theorems for uniform set-partition systems},
journal = {The electronic journal of combinatorics},
year = {2005},
volume = {12},
doi = {10.37236/1937},
zbl = {1075.05086},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1937/}
}
Cité par Sources :