Abstract
Let V be an infinite matrix with rows and columns indexed by the positive integers, and entries in a field F. Suppose that v(i,j) only depends on i - j and is 0 for vertical bar i - j vertical bar large. Then V-n is defined for all n, and one has a "generating function" G = Sigma a(1,1)(V-n)z(n). Ira Gessel has shown that G is algebraic over F(z). We extend his result, allowing v(i),(j) for fixed i - j to be eventually periodic in i rather than constant. This result and some variants of it that we prove will have applications to Hilbert-Kunz theory.