# Random sampling of Latin squares via binary contingency tables and probabilistic divide-and-conquer

## TL;DR

This paper introduces a new probabilistic divide-and-conquer method for uniformly sampling Latin squares of order n by decomposing the problem into binary contingency tables at multiple levels, leveraging Boltzmann sampling heuristics.

## Contribution

It presents a novel algorithm that combines divide-and-conquer with binary contingency tables and Boltzmann sampling to efficiently generate Latin squares.

## Key findings

- The method effectively samples Latin squares of various sizes.
- It demonstrates improved efficiency over existing sampling techniques.
- The approach is adaptable to other combinatorial structures.

## Abstract

We demonstrate a novel approach for the random sampling of Latin squares of order~$n$ via probabilistic divide-and-conquer. The algorithm divides the entries of the table modulo powers of $2$, and samples a corresponding binary contingency table at each level. The sampling distribution is based on the Boltzmann sampling heuristic, along with probabilistic divide-and-conquer.