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HADAMARD MATRICES AND 1-FACTORIZATIONS OF COMPLETE GRAPHS

Published online by Cambridge University Press:  11 February 2019

Keith Ball
Affiliation:
Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, U.K. email [email protected]
Oscar Ortega-Moreno
Affiliation:
Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, U.K. email [email protected]
Maria Prodromou
Affiliation:
Mathematics Department, Westminster Academy, The Naim Dangoor Centre, 255 Harrow Road, London W2 5EZ, U.K. email [email protected]
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Abstract

We discuss 1-factorizations of complete graphs that “match” a given Hadamard matrix. We prove the existence of these factorizations for two families of Hadamard matrices: Walsh matrices and certain Paley matrices.

Type
Research Article
Copyright
Copyright © University College London 2019 

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Footnotes

Oscar Ortega-Moreno was supported by the Mexican National Council of Science and Technology (CONACYT) grant #579817.

References

Moree, P., On primes in arithmetic progression having a prescribed primitive root. J. Number Theory 78(1) 1999, 8598.Google Scholar
Paley, R. E., On orthogonal matrices. Stud. Appl. Math. 12(1–4) 1933, 311320.Google Scholar