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

作者：Cangul Ismail Naci^*; Cevik Ahmet Sinan; Simsek Yilmaz

来源：Boundary Value Problems, 2013, 2013(1): 51.

DOI：10.1186/1687-2770-2013-51

• efficiency
• p-Cockcroft property
• split extension
• generating functions
• Stirling numbers
• array polynomials

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.

• 出版日期2013-3-14