Quasi-regular semilattices in singular linear spaces (Q2798317)

It is well known that lattice is an important part of poset's theory. Its theory plays an important role in many branches of mathematics. In this paper, the authors construct a new quasi-regular semilattice in the singular linear space and compute its parameters.NEWLINENEWLINELet \(F_{q}^{n+l}\) denote the \((n+l)\)-dimensional singular linear space over a finite field \(F_{q}\). For a fixed integer \(m\leq \min\{n,l\}\), denote by \( L_{o}^{m}(F_{q}^{n+l})\) the set of all subspaces of type \((t,t_{1})\), where \( t_{1}\leq t\leq m\). Partially ordered by ordinary inclusion, a family of quasi-regular semilattices is obtained. Moreover, the authors compute all its parameters.