Erdős–Ko–Rado theorem for vector spaces over residue class rings

Abstract

Let [Formula: see text] be its decomposition into a product of powers of distinct primes, and [Formula: see text] be the residue class ring modulo [Formula: see text]. Let [Formula: see text] be the [Formula: see text]-dimensional row vector space over [Formula: see text]. A generalized Grassmann graph over [Formula: see text], denoted by [Formula: see text] ([Formula: see text] for short), has all [Formula: see text]-subspaces of [Formula: see text] as its vertices, and two distinct vertices are adjacent if their intersection is of dimension [Formula: see text], where [Formula: see text]. In this paper, we determine the clique number and geometric structures of maximum cliques of [Formula: see text]. As a result, we obtain the Erdős–Ko–Rado theorem for [Formula: see text].