Properties and Applications of the Recurrence $F( {i + 1,k + 1,n + 1} ) = q^{k + 1} F( {i,k + 1,n} ) - q^k F( {i,k,n} )$

Abstract

The above recurrence formula occurs in the algebraic theory of certain association schemes. Explicit solutions are given in terms of Gaussian binomial coefficients. In particular, some generalized Krawtchouk and Eberlein polynomials are examined in this context.