Applications of the Wulff construction to the number theory

TL;DR

This paper explores how the Wulff construction, a geometric method, can be used to estimate the number of partitions and plane partitions of integers, linking geometric variational problems to combinatorial enumeration.

Contribution

It introduces a novel application of the Wulff construction to combinatorics, providing new geometric tools for estimating partition counts.

Findings

Derived estimates for the number of integer partitions

Extended the Wulff construction to plane partitions

Established connections between geometry and combinatorial enumeration

Abstract

We apply the geometric construction of solutions of some variational problems of combinatorics to estimate the number of partitions and of plane partitions of an integer.