LAUSR

Autoparatopisms of Quasigroups and Latin Squares

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1 Published in 2017 at "Journal of Combinatorial Designs"

DOI: 10.1002/jcd.21515

Abstract: Paratopism is a well-known action of the wreath product Sn≀S3 on Latin squares of order n. A paratopism that maps a Latin square to itself is an autoparatopism of that Latin square. Let Par(n) denote… read more here.

Keywords: autoparatopisms quasigroups; latin squares; latin square; quasigroups latin ... See more keywords

The enumeration of cyclic mutually nearly orthogonal Latin squares

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0 Published in 2019 at "Journal of Combinatorial Designs"

DOI: 10.1002/jcd.21647

Abstract: In this paper, we study collections of mutually nearly orthogonal Latin squares (MNOLS), which come from a modification of the orthogonality condition for mutually orthogonal Latin squares. In particular, we find the maximum μ such… read more here.

Keywords: nearly orthogonal; mutually nearly; mnols order; cyclic mnols ... See more keywords

All group‐based latin squares possess near transversals

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1 Published in 2020 at "Journal of Combinatorial Designs"

DOI: 10.1002/jcd.21701

Abstract: In a latin square of order n, a near transversal is a collection of n −1 cells which intersects each row, column, and symbol class at most once. A longstanding conjecture of Brualdi, Ryser, and Stein… read more here.

Keywords: group; latin squares; based latin; latin square ... See more keywords

Locally repairable codes based on permutation cubes and Latin squares

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1 Published in 2022 at "IEEE Access"

DOI: 10.1109/access.2022.3143899

Abstract: The importance of Locally Repairable Codes (LRCs) lies on their applications in distributed storage systems (DSSs). There are two approaches to repair multiple failed nodes: the parallel approach, in which a set of failed nodes… read more here.

Keywords: permutation cubes; latin squares; repairable codes; locally repairable ... See more keywords

A New Chaotic Image Encryption Algorithm Based on Transversals in a Latin Square

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1 Published in 2022 at "Entropy"

DOI: 10.3390/e24111574

Abstract: In this paper, a new combinatorial structure is introduced for image encryption, which has an excellent encryption effect on security and efficiency. An n-transversal in a Latin square has the function of classifying all the… read more here.

Keywords: latin square; encryption; image encryption; latin squares ... See more keywords

An Efficient Algorithm for Eigenvalue Problem of Latin Squares in a Bipartite Min-Max-Plus System

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1 Published in 2020 at "Symmetry"

DOI: 10.3390/sym12020311

Abstract: In this paper, we consider the eigenproblems for Latin squares in a bipartite min-max-plus system. The focus is upon developing a new algorithm to compute the eigenvalue and eigenvectors (trivial and non-trivial) for Latin squares… read more here.

Keywords: min max; squares bipartite; plus system; bipartite min ... See more keywords

Trivial and Nontrivial Eigenvectors for Latin Squares in Max-Plus Algebra

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1 Published in 2022 at "Symmetry"

DOI: 10.3390/sym14061101

Abstract: A square array whose all rows and columns are different permutations of the same length over the same symbol set is known as a Latin square. A Latin square may or may not be symmetric.… read more here.

Keywords: latin square; latin squares; trivial nontrivial; nontrivial eigenvectors ... See more keywords