Intersection numbers of Sudoku latin squares

TL;DR

This paper characterizes the possible intersection counts of two Sudoku-constrained Latin squares of size n, where n equals the product of grid dimensions h and w.

Contribution

It provides a complete determination of the intersection number set for Sudoku Latin squares, extending classical Latin square intersection theory.

Findings

Identifies all feasible intersection numbers for Sudoku Latin squares.

Extends classical Latin square intersection results to Sudoku constraints.

Provides a framework for analyzing intersections in constrained combinatorial designs.

Abstract

Let $n=hw$, where $h$ and $w$ are integers with $h,w \ge 2$. We determine the set of possible intersection numbers of two $n \times n$ latin squares having the additional `Sudoku' constraint based on a $w \times h$ grid of $h \times w$ boxes.