✦ LIBER ✦

Latin squares with no small odd plexes

✍ Scribed by Judith Egan; Ian M. Wanless

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 242 KB
Volume: 16
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20178

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

A k‐plex in a Latin square of order n is a selection of kn entries in which each row, column, and symbol is represented precisely k times. A transversal of a Latin square corresponds to the case k = 1. We show that for all even n > 2 there exists a Latin square of order n which has no k‐plex for any odd $k < \lfloor {n\over 4} \rfloor$ but does have a k‐plex for every other $k \le {1\over 2} n$. © 2008 Wiley Periodicals, Inc. J Combin Designs 16: 477–492, 2008

📜 SIMILAR VOLUMES

Bachelor latin squares with large indivi

Bachelor latin squares with large indivisible plexes

✍ Judith Egan 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 116 KB

In a latin square of order n, a k-plex is a selection of kn entries in which each row, column, and symbol occurs k times. A 1-plex is also called a transversal. A k-plex is indivisible if it contains no c-plex for 0<c<k. We prove that, for all n ≥ 4, there exists a latin square of order n that can b