Partitions of the set of natural numbers and symplectic homology

TL;DR

This paper proves Tamura's theorem on partitions of positive integers by employing positive -equivariant symplectic homology, extending classical results like Rayleigh-Beatty theorem.

Contribution

It introduces a novel proof of Tamura's theorem using symplectic homology, linking number partitions with symplectic topology techniques.

Findings

Tamura's theorem is proven using symplectic homology.

The approach generalizes classical partition theorems.

New connections between number theory and symplectic topology are established.

Abstract

We prove Tamura's theorem on partitions of the set of positive integers (a generalization of the more famous Rayleigh-Beatty theorem) using the positive $\mathbb{S}^1$-equivariant symplectic homology.