Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-06-01T17:49:57.388Z Has data issue: false hasContentIssue false
  • English
  • Français

Adders for the patterned starter in nonabelian groups

Published online by Cambridge University Press:  09 April 2009

Kenneth B. Gross  and
Philip A. Leonard
Kenneth B. Gross
Affiliation:
Louisiana State University Louisiana, 70803, U.S.A.
Philip A. Leonard
Affiliation:
Arizona State University Arizona, 85281, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Starters with adders, in abelian groups of odd order, have been used widely in recent combinatorial constructions, most notably in the study of Room squares. In this paper, constructions of adders for the so-called “patterned starter” are described, for a large class of nonabelian groups of odd order.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 2 , March 1976 , pp. 185 - 193
Copyright
Copyright © Australian Mathematical Society 1976

References

Anderson, B. A. (1973), ‘Finite Topologies and Hamiltonian Paths’, J. Combinatorial Theory Ser. B. 14, 87–93.CrossRefGoogle Scholar
Anderson, B. A. (1974), ‘A Class of Starter Induced 1-Factorizations’, Graphs and Combinatorics, Lecture Notes in Mathematics No. 406 (Springer-Verlag, Berlin-Heidelberg-New York, 1974).Google Scholar
Byleen, K. (1970), ‘On Stanton and Mullin's construction of Room Squares’, Ann. Math. Statist. 41, 1122–1125.CrossRefGoogle Scholar
Feit, W. and Thompson, J. G. (1963), ‘Solvability of Groups of Odd Order’, Pacific J. Math. 13, 775–1029.CrossRefGoogle Scholar
Gross, K. B. (1973), Constructions for inequivalent Room designs (Ph.D. Thesis, University of Southern California, 1973).Google Scholar
Gross, K. B. (1974), ‘Equivalence of Room designs II’, J. Combinatorial Theory Ser. A 17, 299–316.CrossRefGoogle Scholar
Gross, K. B. and Leonard, P. A. (to appear), ‘The Existence of Strong Starters in Cyclic Groups’, Utilitas Math.Google Scholar
Hung, S. H. Y. and Mendelsohn, N. S. (1974), ‘On Howell Designs’, J. Combinatorial Theory Ser. A. 16, 174–198.CrossRefGoogle Scholar
Leonard, P. A. (1974), ‘Adders for patterned starter in some non-abelian groups’, Bull. Austral. Math. Soc. 10, 321–323.CrossRefGoogle Scholar
Mullin, R. C. and Nemeth, E. (1969a), ‘An existence theorem for Room Squares’, Canad. Math. Bull. 12, 493–497.CrossRefGoogle Scholar
Mullin, R. C. and Nemeth, E. (1969b), ‘On furnishing Room squares’, J. Combinatorial Theory Ser. A 7, 266–272.CrossRefGoogle Scholar
Wallis, W. D., Street, A. P. and Wallis, J. S. (1972), Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices, Lecture Notes No. 292 (Springer-Verlag, Berlin-Heidelberg-New York, 1972).CrossRefGoogle Scholar
Wallis, W. D., (1973), ‘On one-factorizations of complete graphs’, J. Austral. Math: Soc. 16, 167–171.CrossRefGoogle Scholar