Three mutually orthogonal idempotent Latin squares of orders 22 and 26
type: Item
instance of: scholarly article
title: Three mutually orthogonal idempotent Latin squares of orders 22 and 26
zbMATH Open document ID: 0851.05030
DOI: 10.1016/0378-3758(95)00073-9
author: R. Julian R. Abel
author: Xiafu Zhang
author: Hangfu Zhang
published in: Journal of Statistical Planning and Inference
publication date: 1996-09-05T00:00:00Z
review text: A Latin square based on \(\{1, 2,\dots, n\}\) is called idempotent if its \((i, i)\) entry is \(i\). It is known (see \textit{F. E. Bennett}, \textit{K. T. Phelps}, \textit{C. A. Rodger} and \textit{L. Zhu} [Constructions of perfect Mendelsohn designs, Discrete Math. 103, No. 2, 139-151 (1992; Zbl 0756.05012)]) that there are three mutually orthogonal idempotent Latin squares of order \(n\) for any integer \(n\geq 5\) and \(n\neq 6, 10, 18, 22, 26\). The authors of the present article show that the result is in fact true for \(n= 22\) and 26, and they construct such Latin squares. They can be used to construct a \((110, 5, 1)\)-PMD and a \((130, 5, 1)\)-PMD (for the notation, see Zbl 0851.05019).
reviewed by: E. J. F. Primrose
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 906647
zbMATH Keywords: Latin square
MaRDI profile type: Publication
full work available at URL: 0378-3758(95)00073-9
OpenAlex ID: W2000020745
cites work: Constructions of perfect Mendelsohn designs
cites work: Q4017168
cites work: Q3728004
description: scientific article; zbMATH DE number 906647