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.
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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 =
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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