Counting skew monomials in the Frobenius skew polynomial ring

Abstract

We study the Frobenius skew polynomial ring over a polynomial ring in finitely many variables and show that growth function associated to the variables and the Frobenius satisfies a linear recurrence. We introduce the concept of Gelfand-Kirillov base for a finitely generated standard graded algebra over the prime field of characteristic p, where p is prime, and show its existence for the polynomial ring.