Pseudo orthogonal Latin squares
-
Shahab Faruqi
,
S. A. Katre
Abstract
Two Latin squares A, B of order n are called pseudo orthogonal if for any 1 ≤ i, j ≤ n there exists a k, 1 ≤ k ≤ n, such that A(i, k) = B(j, k). We prove that the existence of a family of m mutually pseudo orthogonal Latin squares of order n is equivalent to the existence of a family of m mutually orthogonal Latin squares of order n. We also obtain exact values of clique partition numbers of several classes of complete multipartite graphs and of the tensor product of complete graphs.
Note: Originally published in Diskretnaya Matematika (2020) 32, №3, 113–129 (in Russian).
Acknowledgement
The authors thank Bhaskaracharya Pratishthana (Institute of Mathematics), Pune, for certain facilities and A. Zubkov for his helpful comment regarding computational complexity. The second author thanks support from Lokmanya Tilak Chair, S. P. Pune University, for research facilities.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Reduction of the integer factorization complexity upper bound to the complexity of the Diffie–Hellman problem
- Pseudo orthogonal Latin squares
- Panchromatic colorings of random hypergraphs
- On the connectivity of configuration graphs
- Asymptotics with remainder term for moments of the total cycle number of random A-permutation
- On the dependence of the complexity and depth of reversible circuits consisting of NOT, CNOT, and 2-CNOT gates on the number of additional inputs
- Letter to the Editor
Artikel in diesem Heft
- Frontmatter
- Reduction of the integer factorization complexity upper bound to the complexity of the Diffie–Hellman problem
- Pseudo orthogonal Latin squares
- Panchromatic colorings of random hypergraphs
- On the connectivity of configuration graphs
- Asymptotics with remainder term for moments of the total cycle number of random A-permutation
- On the dependence of the complexity and depth of reversible circuits consisting of NOT, CNOT, and 2-CNOT gates on the number of additional inputs
- Letter to the Editor
