Bounds on the Number of Graphical Partitions

TL;DR

This paper investigates the enumeration of graphical partitions, focusing on those lacking known generating functions, by analyzing the generating function for Frobenius partitions to derive new bounds.

Contribution

It introduces new bounds on the number of graphical partitions and explores their relationship with Frobenius partitions, filling gaps where generating functions are unknown.

Findings

Derived bounds for the count of graphical partitions.

Linked graphical partitions to Frobenius partitions through generating functions.

Provided insights into partitions without known generating functions.

Abstract

We narrow in on the number of graphical partitions for which there is no known generating function by manipulating the well known generating function for Frobenius partitions.