Some array polynomials over special monoid presentations

Abstract

In a recent joint paper (Cevik et al. in Hacet. J. Math. Stat., acceptted), the authors have investigated the p-Cockcroft property (or, equivalently, efficiency) for a presentation, say PE, of the semi-direct product of a free abelian monoid rank two by a finite cyclic monoid. Moreover, they have presented sufficient conditions on a special case for PE to be minimal whilst it is inefficient. In this paper, by considering these results, we first show that the presentations of the form PE can actually be represented by characteristic polynomials. After that, some connections between representative characteristic polynomials and generating functions in terms of array polynomials over the presentation PE will be pointed out. Through indicated connections, the existence of an equivalence among each generating function in itself is claimed studied in this paper. © 2013 Cevik et al.; licensee Springer.