## 11 Citations

Approximate Transversals of Latin Squares

- Mathematics
- 2011

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…

Bachelor latin squares with large indivisible plexes

- Mathematics
- 2011

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…

Latin Squares and Their Applications to Cryptography

- Mathematics
- 2016

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

- Mathematics
- 2011

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 of Latin squares and covering radius of sets of permutations

- MathematicsEur. J. Comb.
- 2013

Transversals, Plexes, and Multiplexes in Iterated Quasigroups

- MathematicsElectron. J. Comb.
- 2018

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

- Biology
- 2012

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

- MathematicsDes. 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

- Mathematics
- 2011

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

- MathematicsDes. 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

- MathematicsElectron. J. Comb.
- 2002

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

- MathematicsThe 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…