On a generalization of P(3,n)

TL;DR

This paper introduces a formula for counting the partitions of positive integers into three polygonal numbers using poset representation theory, expanding understanding of number partitions.

Contribution

It provides a novel formula derived from poset representation theory for counting partitions into three polygonal numbers.

Findings

Derived a new formula for partitions into three polygonal numbers

Applied poset representation theory to number partition problems

Enhanced mathematical understanding of polygonal number partitions

Abstract

By using techniques of poset representation theory, we present a formula for the number of partitions of a positive integer into three polygonal numbers.