A COMBINATORIAL APPROACH TO THE STIRLING NUMBERS OF THE FIRST KIND WITH HIGHER LEVEL

Takao Komatsu, Jose L. Ramirez*, Diego Villamizar

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this paper, we investigate a generalization of the classical Stirling numbers of the first kind by considering permutations over tuples with an extra condition on the minimal elements of the cycles. The main focus of this work is the analysis of combinatorial properties of these newobjects. We give general combinatorial identities and some recurrence relations. We also show some connections with other sequences such as poly-Cauchy numbers with higher level and central factorial numbers. To obtain our results, we use pure combinatorial arguments and classical manipulations of formal power series.

Original languageEnglish
Pages (from-to)293-307
Number of pages15
JournalStudia Scientiarum Mathematicarum Hungarica
Volume58
Issue number3
DOIs
Publication statusPublished - Oct 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • Stirling numbers of the first kind
  • combinatorial identities
  • central factorial numbers

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