Şimşek, YılmazÇevik, Ahmet Sinan2022-10-142022-10-142013-03-14Cangül, İ. N. vd. (2013). "A new approach to connect algebra with analysis: Relationships and applications between presentations and generating functions". Boundary Value Problems, 2013.1687-2770https://doi.org/10.1186/1687-2770-2013-51https://boundaryvalueproblems.springeropen.com/articles/10.1186/1687-2770-2013-51http://hdl.handle.net/11452/29096For 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.eninfo:eu-repo/semantics/openAccessMathematicsEfficiencyp-Cockcroft propertySplit extensionGenerating functionsStirling numbersArray polynomialsP-adic integersSemidirect productsInefficient presentationsBernoulli numbersWord problemMonoidsPolynomialsEulerRingArticle0003257220000012-s2.0-848770473032013Mathematics, appliedMathematicsSemigroup; Inverse Semigroup; Word Problem