An atlas of the smaller maps in orientable and nonorientable surfaces:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton <<[u.a.]>>
Chapman & Hall/CRC
2001
|
| Schriftenreihe: | The CRC Press series on discrete mathematics and its applications
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 279 S. graph. Darst. |
| ISBN: | 1584882077 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | AN ATLAS OF THE 1ALLER MAPS IN ORIENTABLE A D NONORIENTABLE SURFACES
DAVID M. JACKSON DEPARTMENT OF COMBINATORICS & OPTIMIZATION UNIVERSITY
OF WATERLOO ONTARIO, CANADA TERRYI.VISENTIN DEPARTMENT OF MATHEMATICS
UNIVERSITY OF WINNEPEG WINNEPEG, CANADA CHAPMAN & HALL/CRC BOCA RATON
LONDON NEW YORK WASHINGTON, D.C. CONTENTS I MAPS 1 1 INTRODUCTION 3 1.1
ORGANIZATION OF THE ATLAS 4 1.1.1 SUMMARY OF THE CONTENT OF THE ATLAS 4
1.1.2 PREPARATION OF THE TABLES : . . 6 1.2 FURTHER READING 6 2 SURFACES
AND MAPS 9 2.1 REPRESENTATION OF MAPS AND SURFACES 9 2.1.1 PRINCIPAL
DEFINITIONS 9 2.1.2 POLYGONAL REPRESENTATION OF ORIENTABLE SURFACES 11
2.1.3 POLYGONAL REPRESENTATION OF NONORIENTABLE SURFACES 12 2.1.4
ROOTING, ASSOCIATED GRAPH AND DUAL 14 2.1.5 THE ENTRY FOR A MAP IN THE
ATLAS 17 2.2 EXAMPLES OF THE DEFINITIONS 18 2.3 USING THE ATLAS 22 2.3.1
EXAMPLE: DO THE VERTEX AND FACE PARTITIONS DETERMINE THE NUM- BER OF
ROOTINGS? 22 2.3.2 EXAMPLE: MAPS WITH THE SAME VERTEX AND FACE
PARTITIONS BUT DIFFERENT ASSOCIATED GRAPHS 23 2.3.3 EXAMPLES OF
NONREALIZABILITY 23 2.4 AN APPLICATION OF FC-REALIZABLE PARTITIONS 25
2.4.1 THE ABSOLUTE GALOIS GROUP 25 2.4.2 BELYI FUNCTIONS 25 CONTENTS THE
AXIOMATIZATION AND THE ENCODING OF MAPS 29 3.1 ORIENTABLE SURFACES 29
3.1.1 AXIOMATIZATION FOR MAPS IN ORIENTABLE SURFACES 29 3.1.2 ENCODING A
MAP AS A PERMUTATION 30 3.1.3 CONSTRUCTION OF THE SET OF ALL ROOTED MAPS
31 3.1.4 DETERMINING THE NUMBER OF ROOTINGS 37 3.2 LOCALLY ORIENTABLE
SURFACES 38 3.2.1 AXIOMATIZATION FOR MAPS IN LOCALLY ORIENTABLE SURFACES
38 3.2.2 ENCODING A MAP AS A PERMUTATION 40 3.2.3 CONSTRUCTING THE SET
OF ALL ROOTED MAPS 41 GENERATING SERIES AND CONJECTURES 47 4.1
GENERATING SERIES FOR HYPERMAPS 47 4.1.1 SCHUR FUNCTIONS AND ZONAL
POLYNOMIALS 47 4.1.2 GENUS SERIES FOR ROOTED HYPERMAPS 48 4.1.3 TWO
ALGEBRAS 50 4.2 SPECIALIZATION TO MAPS 51 4.2.1 THE GENUS SERIES FOR
MAPS IN ORIENTABLE SURFACES 51 4.2.2 THE GENUS SERIES FOR MAPS IN
LOCALLY ORIENTABLE SURFACES . . . . 52 4.3 THE QUADRANGULATION
CONJECTURE 53 4.3.1 AN INFORMAL PRINCIPLE OF ENUMERATIVE COMBINATORICS .
. . . . . 53 4.3.2 BACKGROUND ,- * * * 54 4.3.3 THE CONJECTURE 54 4.3.4
GENERALIZATION TO EULERIAN MAPS AND THE BIJECTION FI 58 4.3.5 SETWISE
ACTION OF THE BIJECTION Q, 60 4.4 THE 6-CONJECTURE 64 4.4.1 BACKGROUND
65 4.4.2 JACK SYMMETRIC FUNCTIONS 65 4.4.3 THE CONJECTURE 67 4.4.4
EXAMPLES 68 II THE ATLAS 71 5 MAPS IN ORIENTABLE SURFACES 73 5.1 GENUS 0
- THE SPHERE 73 5.2 GENUS 1 - THE TORUS 88 5.3 GENUS 2 - THE DOUBLE
TORUS 107 MAPS IN NONORIENTABLE SURFACES 115 6.1 GENUS 1 - THE
PROJECTIVE PLANE 115 6.2 GENUS 2 - THE KLEIN BOTTLE 121 6.3 GENUS 3 -
THE CROSSCAPPED TORUS 127 6.4 GENUS 4 * THE DOUBLY CROSSCAPPED TORUS 135
FACE REGULAR MAPS AND HYPERMAPS 139 7.1 TRIANGULATIONS 139 7.1.1
ORIENTABLE OF GENUS 0 AND 1 139 7.1.2 NONORIENTABLE OF GENUS 1 AND 2 140
7.2 QUADRANGULATIONS 141 7.2.1 ORIENTABLE OFGENUS 0, 1 AND 2 141 7.2.2
NONORIENTABLE OFGENUS 1, 2 AND 3 143 7.3 HYPERMAPS 145 7.3.1 ORIENTABLE
OFGENUS 0, 1 AND 2 146 7.3.2 NONORIENTABLE OFGENUS 1, 2 AND 3 151
ASSOCIATED GRAPHS AND THEIR MAPS 1S3 III TABLES 209 9 NUMBERS OF ROOTED
MAPS 211 9.1 ORIENTABLE: BY VERTEX AND FACE PARTITION 211 9.2
NONORIENTABLE: BY VERTEX AND FACE PARTITION 218 9.3 SUMMARIZED BY EDGES
AND VERTICES 227 9.3.1 ALL MAPS BY NUMBER OF EDGES 227 9.3.2 ALL MAPS BY
NUMBERS OF EDGES AND VERTICES 228 10 NUMBERS OF UNROOTED MAPS 231 10.1
ORIENTABLE: BY VERTEX AND FACE PARTITION 231 10.2 NONORIENTABLE: BY
VERTEX AND FACE PARTITION 234 11 NONREALIZABLE PAIRS OF PARTITIONS 239
11.1 FOR ORIENTABLE SURFACES 239 11.2 FOR NONORIENTABLE SURFACES 243 12
MAP POLYNOMIALS 245 12.1 6-POLYNOMIALS 245 12.1.1 HYPERMAPS 245 12.1.2
MAPS 252 CONTENTS 12.2 GENUS DISTRIBUTIONS 264 BIBLIOGRAPHY 271 NOTATION
275 INDEX 277
|
| any_adam_object | 1 |
| author | Jackson, David M. Visentin, Terry I. |
| author_facet | Jackson, David M. Visentin, Terry I. |
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| author_sort | Jackson, David M. |
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| building | Verbundindex |
| bvnumber | BV024491181 |
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| dewey-full | 511.33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.33 |
| dewey-search | 511.33 |
| dewey-sort | 3511.33 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 1584882077 |
| language | English |
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| series2 | The CRC Press series on discrete mathematics and its applications |
| spelling | Jackson, David M. Verfasser aut An atlas of the smaller maps in orientable and nonorientable surfaces David M. Jackson ; Terry I. Visentin Boca Raton <<[u.a.]>> Chapman & Hall/CRC 2001 279 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The CRC Press series on discrete mathematics and its applications Visentin, Terry I. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018466375&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jackson, David M. Visentin, Terry I. An atlas of the smaller maps in orientable and nonorientable surfaces |
| title | An atlas of the smaller maps in orientable and nonorientable surfaces |
| title_auth | An atlas of the smaller maps in orientable and nonorientable surfaces |
| title_exact_search | An atlas of the smaller maps in orientable and nonorientable surfaces |
| title_full | An atlas of the smaller maps in orientable and nonorientable surfaces David M. Jackson ; Terry I. Visentin |
| title_fullStr | An atlas of the smaller maps in orientable and nonorientable surfaces David M. Jackson ; Terry I. Visentin |
| title_full_unstemmed | An atlas of the smaller maps in orientable and nonorientable surfaces David M. Jackson ; Terry I. Visentin |
| title_short | An atlas of the smaller maps in orientable and nonorientable surfaces |
| title_sort | an atlas of the smaller maps in orientable and nonorientable surfaces |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018466375&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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