Enumeration and Design

330 Pages·1984·17.243 MB·English

by  David M. Jackson (ed.), Scott A. Vanston (ed.)

Enumeration
~ and Design
— -
Edlfedby
David M. Jackson
Scott A.Vanstone ‘

ENUMERATION
AND DESIGN
Academic Press Rapid ManuscriptReproduction
ENUMERATION
AND DESIGN
Edited by
DAVID M. JACKSON
SCOTT A. VANSTONE
Department of Combinatorics and Optimization
UniversityofWaterloo
Waterloo, Ontario, Canada
1984
ACADEMIC PRESS
(HarcourtBraceJovanovich, Publishers)
TORONIO ORLANDO SANDIEGO SANFRANCISCO NEWYORK
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Mainentryundertitle:
Enumerationanddesign
PapersfromaportionoftheSilverJubilee
ConferenceonCombinatorics.UniversityofWaterloo.
June l4-July2. I982.
ISBN0-l2-379I20-0
.Combinatorialdesignsandconfigurations-—
b . 2 c nrial mm.9. LI
Congresses. 3. Combinatorialanalysis—Congresses.
I. Jackson.D. M.(DavidMartin) I942-
II. Vanstone.S.A.(ScottAlexander). I947-
III. SilverJubileeConferenceonCombinatorics
(I982: UniversityofWaterloo)
QAI643.E58 I984 SII162 C84099285-8
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Mainentryundertitle:
Enumerationanddesign.
BasedinpartontheproceedingsoftheSilver
JubileeConferenceonCombinatorics heldatthe
UniversityofWaterloo June I4toJuly2 I982.
I C L.
mi miunpr
2. Combinatorialdesignsandconfigurations—Congre§ses.
I. Jackson David M. II. Vanstone ScottA. III. Silver
JubileeConferenceonCombinatorics(I982:Univelsityof
Waterloo) IV. UniversityofWaterloo
QAI64.8.E58 I984 SH'.6 8448435
ISBN0-l2-379I20-0(alk.paper)
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CONTENTS
Contributors vIl
Preface
Acknowledgments
An Introduction toCombinatorialCommutativeAlgebra
RichardP. Stanley
OntheTheory oft-Designs
RichardM. Wilson
Useand ExtensionofFrobenius‘ Representationof
Partitions SI
George E. Andrews
Orthogonal PolynomialsOld and New. and SomeCombinatorial
Connections 67
RichardAskey
Strongly RegularGraphsand PartialGeometries 85
A. E. BrouwerandJ. H. Van Lint
Combinatorics ofLaguerre Polynomials l23
Dominique Foamand VolkerStrehl
BaerSubplanes in a Finite Projective Planeand Kirkman
Cubes I4]
Ryoh Fuji-Ham
Combinatorial ProofsofCongruences 157
Ira M. Gessel
On Variance-Balanced Block Designswithb= v
SanpeiKageyama
A Characterization ofPartialGeometric Lattices of
Rank4 2l5
Renu LaskarandAlan P. Sprague
vi CONTENTS
Asymptotics for0- l Matriceswith Prescribed
Line Sums 225
Brendan D. McKay
Balanced lncomplete Block Designswith k =6
and A = l 239
W. H. Mills
On the ExistenceofSome Extremal Self-DualCodes 245
Vera Pless
ExistenceofLongCycles in RandomCubicGraphs 25l
R. W. Robinson andN. C. Wormald
Group Divisible DifferenceSets 27l
Di/en K. Ray-Chaudhuri
lndeterminates and Set lntersections 285
H. J. Ryser
TheNumberofColorCyclic Factorizations ofaGraph 297
AllenJ. Srhwenk
ThreeNew Orthogonal Diagonal LatinSquares 313
W. D. Wallis
CONTRIBUTORS
Numbersinparenthesesindicatethepagesonwhichtheauthors’contributions
begin.
George E. Andrews (5|), Department ofMathematics. PennsylvaniaState Uni-
versity, University Park, Pennsylvania [6802. U.S.A.
Richard Askey (67), Department of Mathematics, University of Wisconsin.
Madison. Wisconsin53706, U.S.A.
A. E. Brouwer(85), MathemattscheCentrum, DepartmentofPureMathematics,
2e Boerhaavestraat, 49 Amsterdam, The Netherlands
Dominique Foata (123), De’partement de Mathe'matiques, Universite’de Stras-
bourg. 7rue René-Descartes, F67084Strasbourg, France
Ryoh Fuji-Hara(l4l). InstituteofSocio-Economic Planning, The University of
Tsukuba, Sakura. Ibaraki305, Japan
Ira M. Gessel (l57). Department of Mathematics. Massachusetts Institute of
Technology. Cambridge, Massachusetts02139, U.S.A.
Sanpei Kageyama (I99), Department of Mathematics. Faculty of Education,
Hiroshima University, [-33 Shinonome3-chome, Minami-ku. Hiroshima734.
Japan
Renu Laskar(2l5). DepartmentofMathematics, Clemson University. Clemson.
South Carolina2965], USA.
J. H.vanLint(85). TechnicalUniversityQfEindhoven. P.0. Box5]3, Eindhoven.
The Netherlands
Brendan D. McKay (225). Computer Science Department. Australian National
University. P.0. Box4. Canberra, ACT. 2600, Australia
W. H. Mills(239). Institute/0r DefenceAnalysis, Thane! Road. Princeton, New
Jersey08540, USA.
Vera Pless(245), DepartmentofMathematics, Box4348. UniversityofIllinoisat
Chicago Circle. Chicago, Illinois60680, USA.
Dijen K. Ray-Chaudhuri (27]), Department ofMathematics. The Ohio State
University, Columbus, Ohio432/0, U.S.A.
vii
viii CONTRIBUTORS
R. W. Robinson(25]), DepartmentofMathematics,SouthernIllinoisUniversity.
Carbondale, Illinois6290]. U.S.A.
H.J.Ryser(285),DepartmentofMathematics.CaliforniaInstituteofTechnology,
Pasadena. California9l125. U.S.A.
Allen J. Schwenk (297). United States Naval Academy, Annapolis, Maryland
21402. USA.
Alan P. Sprague (2l5), Department of Computer Science, The Ohio State
University, Columbus, Ohio432l0, U.S.A.
Richard P. Stanley (3), Department ofMathematics. Massachusetts Instituteof
Technology. Cambridge, Massachusetts02/39, U.S.A.
VolkerStrehl(123), Informatik I, Universiliit Erlangen-Nurnberg. Martenstrasse
3, 0-8520Erlangen. FederalRepublicofGermany
W.D.Wallis(3l3),DepartmentofMathematics,StatisticsandComputerScience,
The UniversityofNewcastle. NewSouth Wales2308. Australia
Richard M. Wilson (l9) Department ofMathematics. California Institute of
Technology, Pasadena, California9]I25 U.S.A.
N. C. Wormald (25]), Department of Mathematics, Statistics and Computer
Science, The UniversityofNewcastle. NewSouth Wales2308. Australia