2021/07/14 by Omar Aceval, Paige Beidelman, Aceval, Omar +11
Decision Sciences · Engineering · #05B15 #Combinatorics (math.CO) #FOS: Mathematics #Optimal Experimental Design Methods #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2107.06437
openalex publication_date 2021/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Latin square of order n is an n× n array which contains n distinct symbols exactly once in each row and column. We define the adjacent distance between two adjacent cells (containing integers) to be their difference modulo n, and inner distance of a Latin square to be the minimum of adjacent distances in the Latin square. By first establishing upper bounds and then constructing squares with said inner distance, we found the maximum inner distance of an n × n Latin square to be \lfloor(n-1)/(2)\rfloor. We then studied special kinds of Latin squares such as pandiagonals (also known as Knut-Vik designs), as well as Sudoku Latin squares. This research was conducted at the REU at Moravian College on Research Challenges of Computational and Experimental Mathematics, with support from the National Science Foundation.