Quasi-binomial coefficients stemming from Nakayama algebras

Abstract

It is known that there is a very closed connection between the set of non-isomorphic indecomposable basic Nakayama algebras and the set of admissible sequences. To determine the cardinal number of all nonisomorphic indecomposable basic Nakayama algebras, we describe the cardinal number of the set of all t-length admissible sequences using a new type of integers called quasi-binomial coefficients. Furthermore, we find some intrinsic relations among binomial coefficients and quasi-binomial coefficients.