Year: 2026
Type: preprint
Abstract: This paper establishes a comprehensive combinatorial and arithmetic framework for mixed Stirling and mixed Bell numbers, bridging partition structures, Touchard polynomials, and prime-power congruences. Furthermore, we develop to $p$-adic valuation theory, proving prime-power Touchard congruences and higher-order modulo-$p^2$ refinements that generalize classical arithmetic properties of combinatorial sequences.
Source: arXiv (Cornell University)
Authors: Yaqubi, Daniel, Mirzavaziri, Madjid
Institutions: University of Torbat-e Jam, Ferdowsi University of Mashhad
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204918529