Associated Lah numbers and r-Stirling numbers

2014/04/22 by Hacène Belbachir, Belbachir, Hacene, Imad Eddine Bousbaa +1 · 1 citation
Chemistry · Mathematics · #05A19 #11B73 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality

paper · pdf · doi:10.48550/arxiv.1404.5573

openalex publication_date 2014/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the associated Lah numbers. Some recurrence relations and convolution identities are established. An extension of the associated Stirling and Lah numbers to the r-Stirling and r-Lah numbers are also given. For all these sequences we give combinatorial interpretation, generating functions, recurrence relations, convolution identities. In the sequel, we develop a section on nested sums related to binomial coefficient.

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• Generalized Ordered Set Partitions

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• Multiple Bracket Function, Stirling Number, and Lah Number Identities
• Convolutions for Stirling numbers, Lah numbers, and binomial coefficients
• Generalized r-Lah numbers
• Multi-Lah numbers and multi-Stirling numbers of the first kind
• The Lah Numbers with Higher Level and the Lah Numbers of Order s