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Type-B analogue of Bell numbers using Rota's Umbral calculus approach

Discrete Mathematics 2024-06-25 v1 Combinatorics

Abstract

Rota used the functional L to recover old properties and obtain some new formulas for the Bell numbers. Tanny used Rota's functional L and the celebrated Worpitzky identity to obtain some expression for the ordered Bell numbers, which can be seen as an evident to the fact that the ordered Bell numbers are gamma-positive. In this paper, we extend some of Rota's and Tanny's results to the framework of the set partitions of Coxeter type B.

Keywords

Cite

@article{arxiv.2406.16393,
  title  = {Type-B analogue of Bell numbers using Rota's Umbral calculus approach},
  author = {Eli Bagno and David Garber},
  journal= {arXiv preprint arXiv:2406.16393},
  year   = {2024}
}

Comments

In Proceedings GASCom 2024, arXiv:2406.14588