Completing Partial Latin Squares - Alternative Proof

TL;DR

This paper presents an alternative proof for completing partial Latin squares by employing an extended Hall's marriage theorem, offering a new perspective on solving this combinatorial problem.

Contribution

It introduces a novel proof technique for Latin square completion using an extended form of Hall's marriage theorem, differing from traditional methods.

Findings

Successful completion of partial Latin squares demonstrated

New proof technique provides theoretical insight

Potential for improved algorithms in Latin square problems

Abstract

The problem of completing a partially specified n by n Latin square is solved by an alternative proof, based on filling the rows (or diagonals) from 1 to n, using an extended form of Hall's marriage theorem.