A New Look into the Generating Function for the 
Partition Function ℰ𝒪(𝑛)

Nilufar Mana Begum

doi:https://doi.org/10.14445/22315373/IJMTT-V71I12P102

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 71 | Issue 12 | Year 2025 | Article Id. IJMTT-V71I12P102 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I12P102

A New Look into the Generating Function for the Partition Function ℰ𝒪(𝑛)

Nilufar Mana Begum

Received	Revised	Accepted	Published
03 Oct 2025	07 Nov 2025	29 Nov 2025	15 Dec 2025

Citation :

Nilufar Mana Begum, "A New Look into the Generating Function for the Partition Function ℰ𝒪(𝑛)," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 12, pp. 8-12, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I12P102

Abstract

Let ℰ𝒪(𝑛), denote the number of partitions of 𝑛 where every even part is less than each odd part and ℰ𝒪(𝑛), denote the number of partitions counted by ℰ𝒪(𝑛), in which only the largest even part appears an odd number of times. In our work, the author uses 5-dissections of 𝑞-products and some identities for the Rogers-Ramanujan continued fraction to obtain the exact generating function for ℰ𝒪(10𝑛+8).

Keywords

Partitions, Partition congruences, Rogers-Ramanujan continued fraction.

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