Journal of Integer Sequences, Vol. 23 (2020), Article 20.4.5

The Multivariate Lah and Stirling Numbers

Amine Belkhir
Faculty of Mathematics
BP 32, El Alia 16111
Bab Ezzouar


An ordered partition of {1, 2, ..., n} into k blocks B1, B2, ..., Bk is a partition where the order of blocks is considered. In the present paper, we consider the case that each block Bi has ri copies. Using this extension of ordered set partitions, we introduce a new generalization of the Lah and Stirling numbers of both kinds which called multivariate Lah and Stirling numbers, respectively. We study several combinatorial properties such as explicit formulas, recurrence relations, generating functions, and some convolution identities.

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(Concerned with sequences A008277 A132393 A271703.)

Received October 27 2019; revised versions received March 14 2020; April 7 2020. Published in Journal of Integer Sequences, April 8 2020.

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