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This is a Quantitative Study study.

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October 3, 2025Open Access

Partition Functions and Kurepa Decomposition I: Algebraic computation and some physical Applications

Key Points

Kurepa factorial equivalence sheds light on the Kurepa conjecture and its implications.
The study presents decompositions involving Dobinski and Bell numbers, enhancing algebraic understanding.
Examining distributions reveals new insights into physical phenomena related to partition functions.
Algebraic computations pave the way for further research in combinatorial aspects and their applications.

Abstract

This paper examines the algebraic features of notable polynomial functions and explores their combinatorial aspects by presenting precise decompositions in terms of Dobinski numbers, Bell numbers, and moments generating functions. Additionally, a new equivalence to the Kurepa factorial is developed to help investigate the Kurepa conjecture. In conclusion, we examine several physical phenomena related to Kurepa factorials, occupation number, Fermi-Dirac and Bose-Einstein distributions while exploring their algebraic characteristics.

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Cite This Study

Francis Atta Howard (Sun,) studied this question.

synapsesocial.com/papers/68e02f3cf0e39f13e7fa2618 https://doi.org/https://doi.org/10.48550/arxiv.2509.06077