Signed partitions - A 'balls into urns' approach

Eli Bagno, David Garber

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Using Reiner's definition of Stirling numbers of the second kind for the group of signed permutations, we provide a 'balls into urns' approach for proving a generaliza¬tion of a well-known identity concerning the classical Stirling numbers S(n, k) of the second kind: n xn = £ 5(n, k)-x{x-I)... (a? - A + 1). fc=o We also present a combinatorial proof (based on Feller's coupling) of the defining identity for the Stirling numbers of the first kind in the group of signed permutations. Our proofs are self-contained and accessible also for non-experts.

Original languageEnglish
Pages (from-to)63-71
Number of pages9
JournalBulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
Volume65
Issue number1
StatePublished - 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 Societatea de Stiinte Matematice din Romania. All rights reserved.

Keywords

  • 'balls into urns' approach. 2010 Mathematics Subject Classification: Primary Q5A18
  • Secondary 05A19
  • Stirling number
  • signed partitions

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