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Some restricted partition functions in terms of 2-adic valuation

Sabi Biswas, Nipen Saikia

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.

Some restricted partition functions in terms of 2-adic valuation

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.

Paper Structure

This paper contains 2 sections, 10 theorems, 44 equations.

Table of Contents

  1. Introduction
  2. Representations of partition functions in terms of $v_2(n)$

Key Result

Theorem 2.1

Let for any positive integer $n$ and $|q|<1$, $\bar{p}_o(n)$ denote the number of overpartitions of an positive integer $n$ into odd parts with the generating function given by Then where

Theorems & Definitions (25)

  • Theorem 2.1
  • proof
  • Corollary 2.2
  • proof
  • Remark 2.3
  • Theorem 2.4
  • proof
  • Corollary 2.5
  • proof
  • Remark 2.6
  • ...and 15 more