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Even-Odd partition identities of Göellnitz-Gordon type

Pooneh Afsharijoo

Abstract

In this paper, we prove a theorem which adds a new member to the famous Göellnitz-Gordon identities. We construct a "new system of recurrence formulas" in order to prove it.

Even-Odd partition identities of Göellnitz-Gordon type

Abstract

In this paper, we prove a theorem which adds a new member to the famous Göellnitz-Gordon identities. We construct a "new system of recurrence formulas" in order to prove it.
Paper Structure (2 sections, 4 theorems, 14 equations)

This paper contains 2 sections, 4 theorems, 14 equations.

Table of Contents

  1. Introduction
  2. a new version of Göellnitz-Gordon identities

Key Result

Theorem 1.1

(Göellnitz-Gordon identities) For the integers $n\geq 0$ and $i\in\{1,2\}$ denote by $G_{i}(n)$ the cardinal of $\mathcal{G}_{i}(n)$ and by $G'_{i}(n)$ the cardinal of $\mathcal{G}'_{i}(n).$ we have:

Theorems & Definitions (5)

  • Theorem 1.1
  • Theorem
  • Corollary 1.2
  • Theorem 2.1
  • proof