# Testing isomorphism of circulant objects in polynomial time

## TL;DR

This paper proves that testing isomorphism of circulant objects, which are invariant under a regular cyclic group, can be done efficiently in polynomial time, advancing the understanding of symmetry-based combinatorial problems.

## Contribution

The paper establishes a polynomial-time algorithm for testing isomorphism of circulant objects invariant under regular cyclic groups, a significant step in symmetry-based combinatorial isomorphism problems.

## Key findings

- Isomorphism testing for circulant objects is polynomial-time solvable.
- The result applies to a broad class of combinatorial objects invariant under cyclic groups.
- This advances the computational understanding of symmetry in combinatorial structures.

## Abstract

Let ${\frak K}$ be a class of combinatorial objects invariant with respect to a given regular cyclic group. It is proved that the isomorphism of any two objects $X,Y\in{\frak K}$ can be tested in polynomial time in sizes of $X$ and $Y$.