@article{Kim2025, 
author = {Taekyun Kim and Dae San Kim},
title = {Probabilistic generalization of Spivey-type relation for degenerate Bell polynomials},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {29488-29497},
keywords = {probabilistic degenerate Bell polynomials, probabilistic degenerate r-Bell polynomials, Spivey-type relation},
url = {https://www.sciopen.com/article/10.3934/math.20251295},
doi = {10.3934/math.20251295},
abstract = {Following Spivey's pivotal discovery of a recurrence relation for Bell numbers, significant research has emerged concerning various generalizations of Bell numbers and polynomials. For example, Kim and Kim established a Spivey-type recurrence relation specifically for degenerate Bell and Dowling polynomials. In this paper, we extend this work by deriving a probabilistic generalization of Spivey-type recurrence relations for both degenerate Bell and degenerate    r-Bell polynomials.}
}