Construction of Quasi-Regular Semilattices with Singular Linear Spaces

Abstract

Let \(\mathbb{F}_q^(n+1)\) denote the \((n+l)\)-dimensional projective space over a finite field \(\mathbb{F}_q\). For a fixed integer \(m \leq \min\{n,l\}\), denote by \(\mathcal{L}_o^m(\mathbb{F}_q^{n+1})\) the set of all subspaces of type \((t,t_1)\), where \(t_1 \leq t \leq m\). Partially ordered by ordinary inclusion, one family of quasi-regular semilattices is obtained. Moreover, we compute all its parameters.