# Necklaces and Slimes

## TL;DR

This paper establishes a bijection between binary necklaces with fixed bead counts and certain codes for prime lengths, introducing a novel 'slime migration' map to facilitate this correspondence.

## Contribution

It introduces the 'slime migration' map and proves a bijection between binary necklaces and codes for prime-length sequences, advancing combinatorial understanding.

## Key findings

- Bijection between binary necklaces and codes for prime n
- Introduction of the slime migration map
- New combinatorial tools for necklace analysis

## Abstract

We show there is a bijection between the binary necklaces with $n$ black beads and $k$ white beads and certain $(n,k)$-codes when $n$ is prime. The main idea is to come up with a new map on necklaces called slime migration.