A new approach to connect algebra with analysis: relationships and applications between presentations and generating functions


CANGÜL İ. N. , ÇEVİK A. S. , ŞİMŞEK Y.

BOUNDARY VALUE PROBLEMS, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2013
  • Doi Number: 10.1186/1687-2770-2013-51
  • Title of Journal : BOUNDARY VALUE PROBLEMS
  • Keywords: efficiency, p-Cockcroft property, split extension, generating functions, Stirling numbers, array polynomials, P-ADIC INTEGERS, SEMIDIRECT PRODUCTS, INEFFICIENT PRESENTATIONS, BERNOULLI NUMBERS, WORD PROBLEM, MONOIDS, POLYNOMIALS, EULER, RING, (H

Abstract

For a minimal group (or monoid) presentation P, let us suppose that P satisfies the algebraic property of either being efficient or inefficient. Then one can investigate whether some generating functions can be applied to it and study what kind of new properties can be obtained by considering special generating functions. To establish that, we will use the presentations of infinite group and monoid examples, namely the split extensions Z(n) X Zand Z(2) X Z, respectively. This study will give an opportunity to make a new classification of infinite groups and monoids by using generating functions.