A new approach to connect algebra with analysis: relationships and applications between presentations and generating functions
1 Department of Mathematics, Faculty of Arts and Science, Uludag University, Gorukle Campus, Bursa, 16059, Turkey
2 Department of Mathematics, Faculty of Science, Selçuk University, Campus, Konya, 42075, Turkey
3 Department of Mathematics, Faculty of Art and Science, Akdeniz University, Campus, Antalya, 07058, Turkey
Boundary Value Problems 2013, 2013:51 doi:10.1186/1687-2770-2013-51Published: 14 March 2013
For a minimal group (or monoid) presentation , let us suppose that 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 and , respectively. This study will give an opportunity to make a new classification of infinite groups and monoids by using generating functions.
MSC: 11B68, 11S40, 12D10, 20M05, 20M50, 26C05, 26C10.