Generalized barred preferential arrangements

Document Type : Research Paper


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

2 Department of Hydraulic Engineering, Faculty of Water Sciences, H-6500, Bajcsy-Zsilinszky utca 12–14, University of Public Service Baja, Hungary

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

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


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.


Main Subjects

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  • Receive Date: 12 August 2021
  • Revise Date: 17 January 2022
  • Accept Date: 11 February 2022
  • Published Online: 01 March 2023