R(p,q)-deformed combinatorics: full characterization and illustration
General Mathematics
2019-06-10 v1
Abstract
This paper addresses a theory of R(p,q)-deformed combinatorics in discrete probability. It mainly focuses on R(p,q)-deformed factorials, binomial coefficients, Vandermonde's formula, Cauchy's formula, binomial and negative binomial formulae, factorial and binomial moments, and Stirling numbers. Moreover, the R(p,q)-Stirling numbers of the second kind and the R(p,q)-Bell numbers for graphs are also derived. Related relevant properties are investigated and discussed. Finally, as a concrete illustration, the developed formalism is displayed for the well known generalized q-Quesne deformed quantum algebra to construct the corresponding deformed combinatorics, as a particular case.
Cite
@article{arxiv.1906.03059,
title = {R(p,q)-deformed combinatorics: full characterization and illustration},
author = {Mahouton Norbert Hounkonnou and Fridolin Melong},
journal= {arXiv preprint arXiv:1906.03059},
year = {2019}
}