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

Let h = ∏ i = 1 t p i s i be its decomposition into a product of powers of distinct primes, and ℤ h be the residue class ring modulo h. Let ℤ h n be the n -dimensional row vector space over ℤ h . A generalized Grassmann graph over ℤ h , denoted by G r (m , n , ℤ h) ( G r for short), has all m -subspaces of ℤ h n as its vertices, and two distinct vertices are adjacent if their intersection is of dimension > m − r , where 2 ≤ r ≤ m + 1 ≤ n. In this paper, we determine the clique number and geometric structures of maximum cliques of G r . As a result, we obtain the Erdős–Ko–Rado theorem for ℤ h n . [ABSTRACT FROM AUTHOR]