Journal of Combinatorics

Volume 9 (2018)

Number 4

Combinatorial and arithmetical properties of the restricted and associated Bell and factorial numbers

Pages: 693 – 720

DOI: https://dx.doi.org/10.4310/JOC.2018.v9.n4.a7

Authors

Victor H. Moll (Department of Mathematics, Tulane University, New Orleans, Louisiana, U.S.A.)

José L. Ramírez (Departamento de Matem´aticas, Universidad Nacional de Colombia, Bogata, Colombia)

Diego Villamizar (Department of Mathematics, Tulane University, New Orleans, Louisiana, U.S.A.)

Abstract

Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus of the present article is the analysis of combinatorial and arithmetical properties of them. The results include several combinatorial identities and recurrences as well as some properties of their $p$-adic valuations.

Received 13 May 2016

Published 7 December 2018