Some array polynomials over special monoid presentations

Creative Commons License

Cevik A. S., Das K. C., ŞİMŞEK Y., CANGÜL İ. N.

FIXED POINT THEORY AND APPLICATIONS, vol.2013, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2013
  • Publication Date: 2013
  • Doi Number: 10.1186/1687-1812-2013-44
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: minimality, characteristic polynomials, array polynomials, P-COCKCROFT PROPERTY, SEMIDIRECT PRODUCTS, EXTENSIONS, BERNOULLI, THEOREM, EULER
  • Akdeniz University Affiliated: Yes


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 , 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 to be minimal whilst it is inefficient. In this paper, by considering these results, we first show that the presentations of the form 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 will be pointed out. Through indicated connections, the existence of an equivalence among each generating function in itself is claimed studied in this paper.