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Bibliographic Details
Main Author:	Engel, Konrad (Author)
Format:	Book
Language:	English
Published:	Cambridge [u.a.] Cambridge Univ. Press 1997
Edition:	1. publ.
Series:	Encyclopedia of mathematics and its applications 65
Subjects:	Sperner-Satz
Online Access:	Inhaltsverzeichnis
Physical Description:	IX, 417 S.
ISBN:	0521452066

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MARC


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adam_text	ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS SPERNER THEORY KONRAD ENGEL UNIVERSITAT ROSTOCK, GERMANY CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE PAGE VII 1 INTRODUCTION 1 1.1 SPERNER S THEOREM 1 1.2 NOTATION AND TERMINOLOGY 4 1.3 THE MAIN EXAMPLES 9 2 EXTREMAL PROBLEMS FOR FINITE SETS 16 2.1 COUNTING IN TWO DIFFERENT WAYS 16 2.2 PARTITIONS INTO SYMMETRIC CHAINS 29 2.3 EXCHANGE OPERATIONS AND COMPRESSION 33 2.4 GENERATING FAMILIES 50 2.5 LINEAR INDEPENDENCE 61 2.6 PROBABILISTIC METHODS 71 3 PROFILE-POLYTOPES FOR SET FAMILIES 84 3.1 FULL HEREDITARY FAMILIES AND THE ANTIBLOCKING TYPE 86 3.2 REDUCTION TO THE CIRCLE 90 3.3 CLASSES OF FAMILIES ARISING FROM BOOLEAN EXPRESSIONS 93 4 THE FLOW-THEORETIC APPROACH IN SPERNER THEORY 116 4.1 THE MAX-FLOW MIN-CUT THEOREM AND THE MIN-COST FLOW ALGORITHM 117 4.2 THE A CUTSET PROBLEM * 125 4.3 THE ^-FAMILY PROBLEM AND RELATED PROBLEMS 131 4.4 THE VARIANCE PROBLEM 140 4.5 NORMAL POSETS AND FLOW MORPHISMS 148 4.6 PRODUCT THEOREMS 166 5 MATCHINGS, SYMMETRIC CHAIN ORDERS, AND THE PARTITION LATTICE 179 5.1 DEFINITIONS, MAIN PROPERTIES, AND EXAMPLES 179 5.2 MORE PART SPERNER THEOREMS AND THE LITTLEWOOD-OFFORD PROBLEM 187 5.3 COVERINGS BY INTERVALS AND SC-ORDERS 194 5.4 SEMISYMMETRIC CHAIN ORDERS AND MATCHINGS 198 VI CONTENTS 6 ALGEBRAIC METHODS IN SPERNER THEORY 208 6. 1 THE FULL RANK PROPERTY AND JORDAN FUNCTIONS 209 6.2 PECK POSETS AND THE COMMUTATION RELATION 229 6.3 RESULTS FOR MODULAR, GEOMETRIC, AND DISTRIBUTIVE LATTICES 248 6.4 THE INDEPENDENCE NUMBER OF GRAPHS AND THE ERDOS-KO-RADO THEOREM 276 6.5 FURTHER ALGEBRAIC METHODS TO PROVE INTERSECTION THEOREMS 295 7 LIMIT THEOREMS AND ASYMPTOTIC ESTIMATES 304 7. 1 CENTRAL AND LOCAL LIMIT THEOREMS 304 7.2 OPTIMAL REPRESENTATIONS AND LIMIT SPERNER THEOREMS 317 7.3 AN ASYMPTOTIC ERDOS-KO-RADO THEOREM 328 8 MACAULAY POSETS 332 8.1 MACAULAY POSETS AND SHADOW MINIMIZATION 333 8.2 EXISTENCE THEOREMS FOR MACAULAY POSETS 351 8.3 OPTIMIZATION PROBLEMS FOR MACAULAY POSETS 356 8.4 SOME FURTHER NUMERICAL AND EXISTENCE RESULTS FOR CHAIN PRODUCTS 367 8.5 SPERNER FAMILIES SATISFYING ADDITIONAL CONDITIONS IN CHAIN PRODUCTS 378 NOTATION 390 BIBLIOGRAPHY 395 INDEX 413
any_adam_object	1
author	Engel, Konrad
author_facet	Engel, Konrad
author_role	aut
author_sort	Engel, Konrad
author_variant	k e ke
building	Verbundindex
bvnumber	BV011362988
classification_rvk	SK 150 SK 170
ctrlnum	(OCoLC)833101301 (DE-599)BVBBV011362988
dewey-full	511.32
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	511 - General principles of mathematics
dewey-raw	511.32
dewey-search	511.32
dewey-sort	3511.32
dewey-tens	510 - Mathematics
discipline	Mathematik
edition	1. publ.
format	Book
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id	DE-604.BV011362988
illustrated	Not Illustrated
indexdate	2024-07-09T18:08:30Z
institution	BVB
isbn	0521452066
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-007637039
oclc_num	833101301
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owner	DE-12 DE-739 DE-703 DE-11 DE-188
owner_facet	DE-12 DE-739 DE-703 DE-11 DE-188
physical	IX, 417 S.
publishDate	1997
publishDateSearch	1997
publishDateSort	1997
publisher	Cambridge Univ. Press
record_format	marc
series	Encyclopedia of mathematics and its applications
series2	Encyclopedia of mathematics and its applications
spelling	Engel, Konrad Verfasser aut Sperner theory Konrad Engel 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1997 IX, 417 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 65 Sperner-Satz (DE-588)4128925-0 gnd rswk-swf Sperner-Satz (DE-588)4128925-0 s DE-604 Encyclopedia of mathematics and its applications 65 (DE-604)BV000903719 65 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007637039&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Engel, Konrad Sperner theory Encyclopedia of mathematics and its applications Sperner-Satz (DE-588)4128925-0 gnd
subject_GND	(DE-588)4128925-0
title	Sperner theory
title_auth	Sperner theory
title_exact_search	Sperner theory
title_full	Sperner theory Konrad Engel
title_fullStr	Sperner theory Konrad Engel
title_full_unstemmed	Sperner theory Konrad Engel
title_short	Sperner theory
title_sort	sperner theory
topic	Sperner-Satz (DE-588)4128925-0 gnd
topic_facet	Sperner-Satz
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007637039&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000903719
work_keys_str_mv	AT engelkonrad spernertheory

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