On cyclically shifted strings

TL;DR

This paper investigates the number of strings with a specific cyclic shift order, a problem relevant to quantum mechanics of spin systems, providing a mathematical solution to count such strings.

Contribution

It introduces a novel approach to determine the count of strings with a given cyclic shift order, connecting combinatorics with quantum physics applications.

Findings

Derived formulas for counting strings of a given order

Established connections between string orders and quantum spin systems

Provided mathematical tools for analyzing cyclically shifted strings

Abstract

If a string is cyclically shifted it will re-appear after a certain number of shifts, which will be called its order. We solve the problem of how many strings exist with a given order. This problem arises in the context of quantum mechanics of spin systems.