Alladi Ramakrishnan Hall

Counting Subspaces in Relation to a Linear Operator

Amritanshu Prasad

IMSc

I will discuss two enumerative problems on subspaces involving a matrix T over a finite field. The first is the problem of counting the number of T-invariant flags of subspaces. The second involves counting subspaces that transform under T in a specified manner. The second problem was introduced by Bender, Coley, Robbins and Rumsey in 1992, but has seen some recent development in my work with Samrith Ram.