### Erdős-Ko-Rado theorem and bilinear forms graphs for matrices over residue class rings [article]

Jun Guo
<span title="2020-02-10">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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 1≤ r≤ m≤ n and Z_h^m× n be the set of all m× n matrices over Z_h. The generalized bilinear forms graph over Z_h, denoted by Bil_r(Z_h^m× n), has the vertex set Z_h^m× n, and two distinct vertices A and B are adjacent if the inner rank of A-B is less than or equal to r. In this paper, we determine the clique number and geometric structures of maximum cliques of
more &raquo; ... l_r(Z_h^m× n). As a result, the Erdős-Ko-Rado theorem for Z_h^m× n is obtained.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2002.03560v1">arXiv:2002.03560v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/765th7chwfczpf2mq2duzhpjsu">fatcat:765th7chwfczpf2mq2duzhpjsu</a> </span>
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