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

2020/03/03 by Jun Guo, Guo, Jun
Mathematics · Computer Science · #Finite Group Theory Research #Rings, Modules, and Algebras #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2003.01292

Abstract

Let h=∏_i=1^tp_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_hⁿ be the n-dimensional row vector space over ℤ_h. A generalized Grassmann graph for ℤ_hⁿ, denoted by G_r(m,n,ℤ_h) (G_r for short), has all m-subspaces of ℤ_hⁿ 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_hⁿ.

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