PreprintCC BY 4.0arXiv
Prime and Touchard Congruences of Mixed-Type Bell Numbers
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-p2 refinements that generalize classical arithmetic properties of combinatorial sequences.
Related
- Identities and congruences involving orthogonal polynomials and Apéry-like numbers
- Prime-power congruences for level-one eigenforms
- Ramanujan-type congruences for the smallest parts function
- The topological Bárány-Larman conjecture for prime numbers
- Parallel Searching Method for Verifying Finiteness of Prime Numbers Presented as Specific Linear Combinations of Factorials
BibTeX
@misc{yaqubi2026prime,
title = {{Prime and Touchard Congruences of Mixed-Type Bell Numbers}},
author = {Daniel Yaqubi and Madjid Mirzavaziri},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30097},
eprint = {2608.30097},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30097},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Prime and Touchard Congruences of Mixed-Type Bell Numbers
AU - Daniel Yaqubi
AU - Madjid Mirzavaziri
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30097
UR - https://arxiv.org/abs/2608.30097
AB - 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.
ER -