Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-25T02:40:55.011Z Has data issue: false hasContentIssue false
  • English
  • Français

HADAMARD MATRICES AND 1-FACTORIZATIONS OF COMPLETE GRAPHS

Part of: Finite fields and commutative rings (number-theoretic aspects) Graph theory Designs and configurations

Published online by Cambridge University Press:  11 February 2019

Keith Ball ,
Oscar Ortega-Moreno  and
Maria Prodromou
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]
Get access

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.

MSC classification

Primary: 05B20: Matrices (incidence, Hadamard, etc.) 05C70: Factorization, matching, partitioning, covering and packing 11T99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 65 , Issue 3 , 2019 , pp. 488 - 499
Copyright
Copyright © University College London 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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, 85–98.Google Scholar
Paley, R. E., On orthogonal matrices. Stud. Appl. Math. 12(1–4) 1933, 311–320.Google Scholar