منابع مشابه
Indivisible plexes in latin squares
A k-plex is a selection of kn entries of a latin square of order n in which each row, column and symbol is represented precisely k times. A transversal of a latin square corresponds to the case k = 1. A k-plex is said to be indivisible if it contains no c-plex for any 0 < c < k. We prove that if n = 2km for integers k ≥ 2 and m ≥ 1 then there exists a latin square of order n composed of 2m disj...
متن کاملA generalization of plexes of Latin squares
A k-plex of a latin square is a collection of cells representing each row, column, and symbol precisely k times. The classic case of k = 1 is more commonly known as a transversal. We introduce the concept of a k-weight, an integral weight function on the cells of a latin square whose row, column, and symbol sums are all k. We then show that several non-existence results about k-plexes can been ...
متن کاملIndivisible partitions of latin squares
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. An indivisible k-plex is one that contains no c-plex for 0ocok. For orders n= 2f2,6g, existence of latin squares with a partition into 1-plexes was famously shown in 1960 by Bose, Shrikhande and Parker. A main result of this paper is tha...
متن کاملLatin Squares with No Small Odd Plexes
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 aLatin 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 < n4 but does have a k-plex for every other k ≤ 1 2n. © 2008 Wiley Periodicals, Inc. J Combi...
متن کاملTransversals in Latin Squares
A latin square of order n is an n×n array of n symbols in which each symbol occurs exactly once in each row and column. A transversal of such a square is a set of n entries such that no two entries share the same row, column or symbol. Transversals are closely related to the notions of complete mappings and orthomorphisms in (quasi)groups, and are fundamental to the concept of mutually orthogon...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2009
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-009-9269-z