Let F n+l q denote the (n + l)-dimensional singular linear space over a finite field F q . For a fixed integer m ≤ min{n, l}, denote by L m o (F n+l q ) the set of all subspaces of type (t, t 1 ), where t 1 ≤ t ≤ m. Partially ordered by ordinary inclusion, one family of quasi regular semilattices is obtained. Moreover, we obtain a association schemes and discuss the bound of a M -clique.
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