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.
View PDF on arXiv
11 Citations
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11 Citations

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Indivisible partitions of latin squares
Approximate Transversals of Latin Squares
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Latin Squares and Their Applications to Cryptography
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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
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 of Latin squares and covering radius of sets of permutations
Transversals, Plexes, and Multiplexes in Iterated Quasigroups
TLDR
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
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
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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.
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References

SHOWING 1-10 OF 22 REFERENCES
Indivisible plexes in latin squares
TLDR
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
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 =…
Indivisible partitions of latin squares
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 distinct symbols in sections of rectangular arrays
The number of transversals in a Latin square
TLDR
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
TLDR
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
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…
On transversals in latin squares
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