# A generalization of plexes of Latin squares

@article{Pula2011AGO,
title={A generalization of plexes of Latin squares},
author={Kyle Pula},
journal={Discret. Math.},
year={2011},
volume={311},
pages={577-581}
}
• Kyle Pula
• Published 1 August 2010
• Mathematics
• Discret. Math.
Approximate Transversals of Latin Squares
A latin square of order n is an n × n array whose entries are drawn from an n-set of symbols such that each symbol appears precisely once in each row and column. A transversal of a latin square is a
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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
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A latin square of order-n is an n × n array over a set of n symbols such that every symbol appears exactly once in each row and exactly once in each column. Latin squares encode features of algebraic
Surveys in Combinatorics 2011: Transversals in latin squares: a survey
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 containing no pair of
Latin squares with restricted transversals
• Mathematics
• 2012
We prove that for all odd m≥3 there exists a latin square of order 3 m that contains an (m−1) × m latin subrectangle consisting of entries not in any transversal. We prove that for all even n≥10
Transversals, Plexes, and Multiplexes in Iterated Quasigroups
It is proved that there exists a constant $c(G,k)$ such that if a $d-iterated quasigroup G of order$n$has a$k-multiplex then for large $d$ the number of its $k$-multiplexes is asymptotically equal to c(G-k) \left(\frac{(kn)!}{k!^n}\right)^{d-1}$. Latin Squares with Restricted Transversals • Mathematics • 2012 The original article to which this erratum refers was correctly published online on 1 December 2011. Due to an error at the publisher, it was then published in Journal of Combinatorial Designs 20: Modeling of Growth Kinetics and Characterization of Membrane Mechanics This work has set out to characterize Tetraselmis cells' membrane elasticity through mathematical modeling of Anabaena to investigate the complex multicellular relationships and colony stability when noise is introduced. ## References SHOWING 1-10 OF 22 REFERENCES Indivisible plexes in latin squares • Mathematics Des. Codes Cryptogr. • 2009 It is proved that if n = 2km for integers k ≥ 2 and m ≥ 1 then there exists a latin square of order n composed of 2m disjoint indivisible k-plexes. Latin squares with no small odd plexes • Mathematics • 2008 A k‐plex in a Latin square of order n is a selection of kn entries in which each row, column, and symbol is represented precisely k times. A transversal of a Latin square corresponds to the case k = Bachelor latin squares with large indivisible plexes In a latin square of order n, a k‐plex is a selection of kn entries in which each row, column, and symbol occurs k times. A 1‐plex is also called a transversal. A k‐plex is indivisible if it contains The number of transversals in a Latin square • Mathematics Des. Codes Cryptogr. • 2006 The maximum number of transversals over all Latin squares of order n is shown to be T(n), and an upper bound on the number of placements of n non-attacking queens on an n × n toroidal chess board is found. A Generalisation of Transversals for Latin Squares It is shown that certain latin squares, including the Cayley tables of many groups, are shown to contain no$(2c+1)-plex for any integer $c, and the existence of indivisible$k$-plexes, meaning that they contain no$c$-Plex for$1\leq c.
Discrete Mathematics Using Latin Squares
• P. Shiu
• Mathematics
The Mathematical Gazette
• 2000
LATIN SQUARES. A Brief Introduction to Latin Squares. Mutually Orthogonal Latin Squares. GENERALIZATIONS. Orthogonal Hypercubes. Frequency Squares. RELATED MATHEMATICS. Principle of
Transversals and multicolored matchings
• Mathematics
• 2004
Ryser conjectured that the number of transversals of a latin square of order n is congruent to n modulo 2. Balasubramanian has shown that the number of transversals of a latin square of even order is