Systematic Counting of Restricted Partitions

TL;DR

This paper introduces two systematic methods for counting classes of integer partitions that avoid specified pattern sets, advancing combinatorial enumeration techniques.

Contribution

It presents novel approaches for enumerating pattern-avoiding partitions, expanding the toolkit for combinatorial pattern avoidance analysis.

Findings

Developed two systematic counting methods.

Applied methods to various pattern sets.

Enhanced understanding of pattern-avoiding partitions.

Abstract

Integer partitions are one of the most fundamental objects of combinatorics (and number theory), and so is enumerating objects avoiding patterns. In the present paper we describe two approaches for the systematic counting of classes of partitions avoiding an arbitrary set of "patterns".