English

On the periodicity problem of residual r-Fubini sequences

Number Theory 2017-01-26 v1

Abstract

For any positive integer rr, the rr-Fubini number with parameter nn, denoted by Fn,rF_{n,r}, is equal to the number of ways that the elements of a set with n+rn+r elements can be weak ordered such that the rr least elements are in distinct orders. In this article we focus on the sequence of residues of the rr-Fubini numbers modulo a positive integer ss and show that this sequence is periodic and then, exhibit how to calculate its period length. As an extra result, an explicit formula for the rr-Stirling numbers is obtained which is frequently used in calculations.

Keywords

Cite

@article{arxiv.1701.07276,
  title  = {On the periodicity problem of residual r-Fubini sequences},
  author = {Amir Abbas Asgari and Majid Jahangiri},
  journal= {arXiv preprint arXiv:1701.07276},
  year   = {2017}
}