Some restricted partition functions in terms of 2-adic valuation

TL;DR

This paper explores how certain restricted partition functions can be expressed using 2-adic valuation, providing new insights into their mathematical structure and properties.

Contribution

It introduces novel representations of restricted partition functions in terms of 2-adic valuation, advancing understanding of their number-theoretic characteristics.

Findings

New formulas for restricted partition functions using 2-adic valuation

Enhanced understanding of the 2-adic properties of partition functions

Potential applications in number theory and combinatorics

Abstract

The 2-adic valuation of an integer n which is the exponent of the highest power of 2 that divides n. In this paper, we give representations of certain restricted partition functions in terms of 2-adic valuation.