Combinatorial Mathematics X: Proceedings of the Conference held in Adelaide, Australia, August 23–27, 1982

430 Pages·1983·5.021 MB·English

by  C. C. Chen, N. Quimpo (auth.), Louis Reynolds Antoine Casse (eds.)

Lecture Notes in
Mathematics
Edited by A. Dold and B. Eckmann
Cornb inatorial Mathematics X
Proceedings of the Conference
held in Adelaide, Australia, August 23-27,1982
Edited by L. R. A. Casse
Sp ringer-Verlag
Berlin Heidelberg New York Tokyo I983
Editor
Louis Reynolds Antoine Casse
The University of Adelaide
G.RO., Box 498, Adelaide, South Australia 5001, Australia
AMS Subject Classifications (1980): 05A05, 05A15, 05B 05, 05 B10,
05B15, 05B20, 05B25, 05B30, 05B35, 05B40, 05 B45, 05B50,
05005, 05025, 05C30, 05060, 05065, 05075, 12020, 15A23,
15A33, 20B 22,20 B25, 51E05, 15 E15, 15 E25, 62 K10, 68E10, 90 B35,
94 B05, 94B70
ISBN 3-540-12708-9 Springer-Verlag Berlin Heidelberg New York Tokyo
ISBN 0-387-12708-9 Springer-Verlag New York Heidelberg Berlin Tokyo
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PREFACE
The Tenth Australian Conference on Combinatorial Mathematics
was held at the University of Adelaide from 23rd to 27th August 1982.
The Conference was fortunate enough to hear addresses given by
distinguished combinatorialists: C.C. Chen (Singapore),
J.W.P. Hirschfeld (U.K.), D.A. Holton (Australia), A.D. Keedwell
(U.K.), .C Lindner (U.S.A.), N.J. Pullman (Canada), .D Stinson
(Canada), and J.A. Thas (Belgium). This volume contains the text of
seven of these invited addresses and of twenty-three contributed talks.
M~nuscripts of the remaining contributed talks given at the
conference are to be published elsewhere.
Many people helped with the organisation of the conference and
with the publication of this volume, and we are grateful to all of
them. We thank all those who chaired sessions and refereed papers.
Our special thanks go to the members of the "Ceometry Seminar" and
of the departments of Mathematics at the University of Adelaide.
We particularly acknowledge the generous support of the
following
Australian Mathematical Society
A.N.Z. Bank
Trans Australia Airlines.
The University of Adelaide, the Student Union, and the University
of Adelaide Club allowed us the use of their facilities. Much
financial assistance was provided by the Departments of Applied
Mathematics, Computer Science, Pure Mathematics, and Statistics.
Finally we thank Ms. Henderson, M~s. Renshaw and Mrs. Halsey
for their kindness and typing.
L.R.A. Casse
PARTICIPANTS
Mr. .R Aldred Department of Mathematics,
University of Melbourne,
Parkville, Vic., 3052.
Dr. .J Arkinstall Mathematics and Computing Department,
South Australian Institute of Technology,
Whyalla, S.A., 5600.
Prof. .G Berzsenyi Department of Mathematics,
Lamar University,
Beaumont,
Texas, U.S.A.
Mr. .S Bourn Pure Mathematics Department,
University of Adelaide,
Adelaide, S.A°, 5001.
Dr. D.R. Breach Department of Mathematics,
University of Canterbury~
Christchurch,
New Zealand.
Dr. .R Buttsworth Department of Mathematics,
University of Queensland,
.tS Lucia, Qld., 4067.
Dr. .L Caccetta School of Mathematics and Computing,
Western Australian Institute of Technology,
South Bentley, W.A., 6102.
Dr. .R Casse Department of Pure Mathematics,
University of Adelaide,
Adelaide, S.A., 5001.
Prof. C.C. Chen Department of Mathematics,
National University of Singapore,
Bukit Timah Road,
Singapore, 1025.
Dr. R.J. Clarke Department of Pure Mathematics,
University of Adelaide,
Adelaide, S.A., 5001.
Prof. .J Colbourn Department of Computational Science,
University of Saskatchewan,
Saskatchewan, Saskatoon, S7N 0W0,
Canada.
Dr. M.J. Colbourn Department of Computational Science,
University of Saskatchewan,
Saskatchewan, Saskatoon, S7N 0W0,
Canada.
Dr. W.H. Cornish School of Mathematical Sciences,
The Flinders University of S.A.,
Bedford Park, S.A., 5042.
Dr. E.A. Cousins Department of Applied Mathematics,
University of Adelaide,
Adelaide, S.A., 5001.
Mr. .E Dawson Department of Mathematics,
Queensland Institute of Technology,
P.O. Box 2434,
Brisbane, Qld., 4001.
Mr. .W De Launay Department of Applied Mathematics,
University of Sydney,
Sydney, N.S.W., 2006.
Dr. .P Eades Department of Computing Science,
University of Queensland,
.tS Lucia~ Qld., 4067.
Mr. .M Ellingham Department of Mathematics,
University of Melbourne,
Parkville, Vic., 3052.
Dr. D.G. Glynn Department of Pure Mathematics,
University of Adelaide,
Adelaide, S.A., 5001.
Dr. .J Hammer Department of Pure Mathematics,
University of Sydney,
Sydney, N.S.W., 2006.
Dr. .W Henderson Department of Applied Mathematics,
University of Adelaide,
Adelaide, S.A., 5001.
Dr. .J Hirschfeld School of Mathematics and Physical Sciences,
University of Sussex,
Falmer, Bri~hton~ BNI 9QH,
England.
Dr. D.A. Holton Department of Mathematics,
University of Melbourne,
Parkville, Vic., 3052.
Prof. A.F. horadam Department of Mathematics,
University of New England,
Armidale, N.S.W., 2351.
Mr. .R Johnston Department of Applied Mathematics,
La Trobe University,
Bundoora, Vic., 3083.
.rD A.D. Keedwell Department of Mathematics,
University of Surrey,
Guildford, Surrey, GU2 5XH,
England.
Mr. R.W. Kennington Department of Applied Mathematics,
University of Adelaide,
Adelaide, S.A., 5001.
)V
Mr. .S Kettle Department of Mathematics,
Monash University,
Clayton, Vic., 3168.
Prof. .C Lindner Mathematics Department,
Auburn University,
Auburn, Alabama, 36849,
U.S.A.
Dr. K.L. McAvaney Division of Computing and Mathematics,
Deakin University,
P.O. Box 125,
Belmont, Vic., 3217.
Dr. R.G.J. Mills South Australian Institute of Technology,
P.O. Box ,i
Ingle Farm, S.A., 5098.
Mr. .P O'Halloran School of Information Sciences,
Canberra College of Advanced Education,
P.O. Box ,I
Belconnen, A.C.T., 2600.
Ms. .C O'Keefe Department of Pure Mathematics,
University of Adelaide,
Adelaide, S.A., 5001.
Dr. .D Parrott Department of Pure Mathematics,
University of Adelaide,
Adelaide, S.A., 5001.
Dr. .C Pearce Department of Applied Mathematics,
University of Adelaide,
Adelaide, SoA., 5001.
Mr. .T Pentilla Department of Pure Mathematics,
University of Adelaide,
Adelaide, S.A., 5001.
Dr. B.B. Phadke School of Mathematical Sciences,
The Flinders University of S.A.,
Bedford Park, S.A., 5042.
Dr. E.J. Pitman Department of Pure Mathematics,
University of Adelaide,
Adelaide, S.A., 5001.
Dr. .R Potter 75 Alexander Drive,
River Plaza,
New Jersey, 07701,
U.S.A.
.rD .C Praeger Department of Mathematics,
University of Western Australia,
Nedlands, W.A., 6009.
Prof. N.J. Pullman Queens University,
Kingston,
Ontario, K7L 3N6,
Canada.
IIV
Dr. A.J. Rahilly Gippsland Institute of Advanced Education,
Switchback Road,
Churchill, Vic., 3842.
Dr. .C Rodger Mathematics Department,
Auburn University,
Auburn, Alabama, 36849,
U.S.A.
Dr. .D Rogers Mathematics Department,
The University,
Reading, RG6 2AX,
England.
Dr. .F Salzborn Department of Applied Mathematics,
University of Adelaide,
Adelaide, S.A., 5001.
Dr. .J Seberry Department of Applied Mathematics,
University of Sydney,
Sydney, N.S.W., 2006.
.rD .B Sherman Department of Education,
University of Adelaide,
Adelaide, S.A., 5001.
Mr. R.J. Simpson Department of Pure Mathematics,
University of Adelaide,
Adelaide, S.A., 5001.
Dr. .D Skillicorn Department of Computing Information Sciences,
Queens University,
Kingston,
Ontario, K7L 3N6,
Canada.
Mr. .D Skilton Department of Mathematics,
University of Newcastle,
Shortland, N.S.W., 2303.
Mr. .B Smetaniuk Department of Applied Mathematics,
University of Sydney,
Sydney, N.S.W., 2006.
Dr. D.R. Stinson University of Manitoba,
Winnipeg,
Manitoba, R3T 2N2,
Canada.
Dr; A.P. Street Department of Mathematics,
University of Queensland,
.tS Lucia, Qld., 4067.
Mrs. .M Sved Department of Pure Mathematics,
University of Adelaide,
Adelaide, S.A., 5001.
Mrs. .E Szekeres School of Mathematics,
University of New South Wales,
P.O. Box ,i
Kensington, N.S.W., 2033.
Vlll
Prof. .G Szekeres School of Mathematics,
University of New South Wales,
P.O. Box ,i
Kensington, N.S.W., 2033.
Prof. J.A. Thas Seminar of Geometry and Combinatorics,
University of Ghent,
Krijgslaan 271,
9000 - Ghent,
Belgium.
Mr. .R Turner Department of Mathematics,
University of Melbourne,
Parkville, Vic., 3052.
Dr. .W Venables Department of Statistics,
University of Adelaide,
Adelaide, S.A., 5001.
Prof. W.D. Wallis Department of Mathematics,
University of Newcastle,
Shortland, N.S.W., 2308.
Dr. .A Werner P.O. Box 252,
Elizabeth, S.A., 5112.
Dr. .P Wild Department of Pure Mathematics,
University of Adelaide,
Adelaide, S.A. 5001.
Dr. .N Wormald Department of Mathematics,
University of Newcastle,
Shortland, N.S.W., 2308.
TABLE OF CONTENTS
In the case of co-authored papers, an
asterisk(*) indicates the author who
spoke at the conference
INVITED PAPERS
C.C. Chen* and N. Quimpo:
Hamiltonian Cayley graphs of order pq .
J.W.P. Hirschfeld:
The Weil conjectures in finite geometry.
D.A. Holton:
Cycles in graphs. 24
A.D. Keedwell:
Sequenceable groups, generalized complete
mappings, neofields, and block designs. 49
N.J. Pullman:
Clique coverings of graphs - A survey. 72
.D Stinson:
Room squares and subsquares. 86
J.A. Thas:
Geometries in finite projective spaces:
recent results. 96
CONTRIBUTED PAPERS
.S Bourn:
A canonical form for incidence matrices of
finite projective planes and their
associated Latin squares and planar
ternary rings. 111
.L Caccetta* and N. Pullman:
On clique covering numbers of cubic graphs. 121
R.J. Clarke:
Modelling competitions by poset multiplication. 128
C.J. Colbourn and M.J, Colbourn:
Decomposition of block designs: computational 141
issues.
W.H. Cornish:
A combinatorial problem and the generalized cosh. 147
W. DeLauney:
Generalised Hadamard matrices whose rows and
columns form a group. 154
X
M.N. Ellingham:
The asymptotic connectivity of labelled
coloured regular bipartite graphs. 177
H.M. Gastineau-Hills:
Kronecker products of systems of orthogonal
designs. 189
H.M. Gastineau-Hills and .J Hammer*:
Kronecker products of systems of higher
dimensional orthogonal designs. 206
.D Glynn:
Two new sequences of ovals in finite
Desarguesian planes of even order. 217
W. Henderson, R.W. Kennington and C.E.M. Pearce:
Stochastic processes and combinatoric
identities. 230
S.G. Kettle:
Families enumerated by the Schroder-
Etherington sequence and a renewal array
it generates. 244
S.G. Kettle:
Classifying and enumerating some freely
generated families of objects. 275
K.L. McAvaney:
Composite graphs with edge stability
index one 305
J. Pitman and P. Leske:
A number-theoretical note on Cornish's
paper. 316
C.E. Praeger* and .P Schultz:
On the automorphisms of rooted trees
with height distributions. 319
A. Rahilly and .D Searby:
On partially transitive planes of Hughes
type (6,m) . 335
C.A. Rodger:
Embedding incomplete idempotent Latin squares. 355
B. Smetaniuk:
The completion of partial f-squares. 367
M. Sved:
Baer subspaces in the n-dimensional
projective space. 375
.G Szekeres:
Distribution of labelled trees by diameter. 392
W.D. Wallis* and .L Zhu:
Orthogonal Latin squares with small
subsquares. 398