Title:	Completion properties of partial latin squares
DNr:	LiU-compute-2025-51
Project Type:	LiU Compute
Principal Investigator:	Jan Snellman <jan.snellman@liu.se>
Affiliation:	Linköpings universitet
Duration:	2026-02-01 – 2026-08-01
Classification:	10104
Keywords:

Abstract

This is a Bachelor's thesis project, advisor professor Carl Johan Casselgren (MAI), student Andreas Stenmark andst152@student.liu.se, examiner Jan Snellman (MAI). The project is guided by the following central questions: 1. Are partial Latin squares with two filled rows, one filled column, and one distinguished symbol always completable, except possibly for finitely many small orders? 2. What structural constraints emerge when this class is normalized by isotopy, and how do these constraints indicate possible obstructions to completion? 3. For small values of n, which normalized instances are completable, and what patterns arise from exhaustive computational testing? 4. Based on computational evidence, what conjecture best captures the completability behaviour of this class for general n? 5. Which structural conditions provably guarantee completability within this class, and can these be established using theoretical arguments? 6. Can techniques analogous to those used in the RCS and PLS(2, 3; n) settings be adapted to support a general completability result for this new class?