Generalized Barred Preferential Arrangements

Document Type : Research Paper

Authors

1 Departamento de Métodos Estadı́sticos, Facultad de Ciencias, Universidad Zaragoza, C. de Pedro Cerbuna, 12, 50009, Zaragoza, Spain

2 Faculty of Water Sciences, University of Public Service, Budapest, Hungary

3 Department of Mathematics, Rhodes University, Grahamstown, 6139, South Africa

4 Department of Mathematical Sciences, Sol Plaatje University, Kimberley, 8301, South Africa

Abstract

We investigate a generalization of Fubini numbers. We present the combinatorial interpretation as barred preferential arrangements with some additional conditions on the blocks. We provide a proof for a generalization of Nelsen's Theorem. We consider these numbers from a probabilistic view point and demonstrate how they can be written in terms of the expectation of random descending factorial involving the negative binomial process.

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