Lecture 4 : 3 SAT and Latin Squares

The Search for Systems of Diagonal Latin Squares Using the SAT@home Project

In this paper we consider the approach to solving the problem of search for systems of diagonal orthogonal Latin squares in the form of the Boolean Satisfiability problem. We describe two different propositional encodings that we use. The first encoding is constructed for finding pairs of orthogonal diagonal Latin squares of order 10. Using this encoding we managed to find 17 previously unknown...

Completing Quasigroups or Latin Squares: A Structured Graph Coloring Problem

We introduce a graph coloring challenge benchmark based on the problem of completing Latin squares. We show how the hardness of the instances can be finely controlled by varying the fraction of precolored squares. We compare three complete (exact) solution strategies on this benchmark: (1) a Constraint Satisfaction (CSP) based approach, (2) a hybrid Linear Programming / CSP approach, and (3) a ...

Lecture 9 : Latin Squares and Geometry Week 9 UCSB

Lecture 5 : Latin Squares and Magic

Today's application is to magic! Not the friendship kind, though 1 ; instead, we're going to talk about magic squares, an incredibly old piece of mathematics that we can study using Latin squares. Definition. A magic square is a n × n grid filled with the integers {0, 1,. .. n 2 − 1}, such that • each number is used exactly once in our entire grid, and • the sum of all of the entries along any ...

On the existence of 3-way k-homogeneous Latin trades

A μ-way Latin trade of volume s is a collection of μ partial Latin squares T1, T2, . . . , Tμ, containing exactly the same s filled cells, such that if cell (i, j) is filled, it contains a different entry in each of the μ partial Latin squares, and such that row i in each of the μ partial Latin squares contains, set-wise, the same symbols and column j, likewise. It is called μ–way k–homogeneous...