Erdős-Ko-Rado-Type Theorems for Colored Sets

Abstract

An Erdős-Ko-Rado-type theorem was established by Bollobás and Leader for $q$-signed sets and by Ku and Leader for partial permutations. In this paper, we establish an LYM-type inequality for partial permutations, and prove Ku and Leader's conjecture on maximal $k$-uniform intersecting families of partial permutations. Similar results on general colored sets are presented.