Grassmannians over a finite field

Abstract

In this paper, we characterize the Grassmannian Gr$(d,n)$ in terms of the row echelon forms of rank $d$. Using this characterization, then in the case of finite field we give a polynomial-type formula for the cardinality of the Grassmannian.

5 pages

References in corpus (1)

• The space $L^2$ on semi-infinite Grassmannian over finite field