An Introduction to Convex Polytopes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1983
|
| Schriftenreihe: | Graduate Texts in Mathematics
90 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The aim of this book is to introduce the reader to the fascinating world of convex polytopes. The highlights of the book are three main theorems in the combinatorial theory of convex polytopes, known as the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. All the background information on convex sets and convex polytopes which is m~eded to under stand and appreciate these three theorems is developed in detail. This background material also forms a basis for studying other aspects of polytope theory. The Dehn-Sommerville Relations are classical, whereas the proofs of the Upper Bound Theorem and the Lower Bound Theorem are of more recent date: they were found in the early 1970's by P. McMullen and D. Barnette, respectively. A famous conjecture of P. McMullen on the charac terization off-vectors of simplicial or simple polytopes dates from the same period; the book ends with a brief discussion of this conjecture and some of its relations to the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. However, the recent proofs that McMullen's conditions are both sufficient (L. J. Billera and C. W. Lee, 1980) and necessary (R. P. Stanley, 1980) go beyond the scope of the book. Prerequisites for reading the book are modest: standard linear algebra and elementary point set topology in [R1d will suffice |
| Beschreibung: | 1 Online-Ressource (VIII, 162 p) |
| ISBN: | 9781461211488 9781461270232 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-1148-8 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042419767 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1983 |||| o||u| ||||||eng d | ||
| 020 | |a 9781461211488 |c Online |9 978-1-4612-1148-8 | ||
| 020 | |a 9781461270232 |c Print |9 978-1-4612-7023-2 | ||
| 024 | 7 | |a 10.1007/978-1-4612-1148-8 |2 doi | |
| 035 | |a (OCoLC)863760231 | ||
| 035 | |a (DE-599)BVBBV042419767 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 511.6 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Brøndsted, Arne |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An Introduction to Convex Polytopes |c by Arne Brøndsted |
| 264 | 1 | |a New York, NY |b Springer New York |c 1983 | |
| 300 | |a 1 Online-Ressource (VIII, 162 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Graduate Texts in Mathematics |v 90 |x 0072-5285 | |
| 500 | |a The aim of this book is to introduce the reader to the fascinating world of convex polytopes. The highlights of the book are three main theorems in the combinatorial theory of convex polytopes, known as the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. All the background information on convex sets and convex polytopes which is m~eded to under stand and appreciate these three theorems is developed in detail. This background material also forms a basis for studying other aspects of polytope theory. The Dehn-Sommerville Relations are classical, whereas the proofs of the Upper Bound Theorem and the Lower Bound Theorem are of more recent date: they were found in the early 1970's by P. McMullen and D. Barnette, respectively. A famous conjecture of P. McMullen on the charac terization off-vectors of simplicial or simple polytopes dates from the same period; the book ends with a brief discussion of this conjecture and some of its relations to the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. However, the recent proofs that McMullen's conditions are both sufficient (L. J. Billera and C. W. Lee, 1980) and necessary (R. P. Stanley, 1980) go beyond the scope of the book. Prerequisites for reading the book are modest: standard linear algebra and elementary point set topology in [R1d will suffice | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Combinatorics | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Konvexe Menge |0 (DE-588)4165212-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Konvexes Polytop |0 (DE-588)4367579-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Konvexer Körper |0 (DE-588)4165214-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Konvexes Polytop |0 (DE-588)4367579-7 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Konvexe Menge |0 (DE-588)4165212-5 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 689 | 2 | 0 | |a Konvexer Körper |0 (DE-588)4165214-9 |D s |
| 689 | 2 | |8 3\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4612-1148-8 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027855184 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153090791702528 |
|---|---|
| any_adam_object | |
| author | Brøndsted, Arne |
| author_facet | Brøndsted, Arne |
| author_role | aut |
| author_sort | Brøndsted, Arne |
| author_variant | a b ab |
| building | Verbundindex |
| bvnumber | BV042419767 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863760231 (DE-599)BVBBV042419767 |
| dewey-full | 511.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1148-8 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03327nmm a2200541zcb4500</leader><controlfield tag="001">BV042419767</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1983 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461211488</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4612-1148-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461270232</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4612-7023-2</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4612-1148-8</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863760231</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042419767</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.6</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Brøndsted, Arne</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">An Introduction to Convex Polytopes</subfield><subfield code="c">by Arne Brøndsted</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer New York</subfield><subfield code="c">1983</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (VIII, 162 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Graduate Texts in Mathematics</subfield><subfield code="v">90</subfield><subfield code="x">0072-5285</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The aim of this book is to introduce the reader to the fascinating world of convex polytopes. The highlights of the book are three main theorems in the combinatorial theory of convex polytopes, known as the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. All the background information on convex sets and convex polytopes which is m~eded to under stand and appreciate these three theorems is developed in detail. This background material also forms a basis for studying other aspects of polytope theory. The Dehn-Sommerville Relations are classical, whereas the proofs of the Upper Bound Theorem and the Lower Bound Theorem are of more recent date: they were found in the early 1970's by P. McMullen and D. Barnette, respectively. A famous conjecture of P. McMullen on the charac terization off-vectors of simplicial or simple polytopes dates from the same period; the book ends with a brief discussion of this conjecture and some of its relations to the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. However, the recent proofs that McMullen's conditions are both sufficient (L. J. Billera and C. W. Lee, 1980) and necessary (R. P. Stanley, 1980) go beyond the scope of the book. Prerequisites for reading the book are modest: standard linear algebra and elementary point set topology in [R1d will suffice</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Combinatorics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konvexe Menge</subfield><subfield code="0">(DE-588)4165212-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konvexes Polytop</subfield><subfield code="0">(DE-588)4367579-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konvexer Körper</subfield><subfield code="0">(DE-588)4165214-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Konvexes Polytop</subfield><subfield code="0">(DE-588)4367579-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Konvexe Menge</subfield><subfield code="0">(DE-588)4165212-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Konvexer Körper</subfield><subfield code="0">(DE-588)4165214-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">3\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4612-1148-8</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027855184</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042419767 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461211488 9781461270232 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855184 |
| oclc_num | 863760231 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (VIII, 162 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Graduate Texts in Mathematics |
| spelling | Brøndsted, Arne Verfasser aut An Introduction to Convex Polytopes by Arne Brøndsted New York, NY Springer New York 1983 1 Online-Ressource (VIII, 162 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 90 0072-5285 The aim of this book is to introduce the reader to the fascinating world of convex polytopes. The highlights of the book are three main theorems in the combinatorial theory of convex polytopes, known as the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. All the background information on convex sets and convex polytopes which is m~eded to under stand and appreciate these three theorems is developed in detail. This background material also forms a basis for studying other aspects of polytope theory. The Dehn-Sommerville Relations are classical, whereas the proofs of the Upper Bound Theorem and the Lower Bound Theorem are of more recent date: they were found in the early 1970's by P. McMullen and D. Barnette, respectively. A famous conjecture of P. McMullen on the charac terization off-vectors of simplicial or simple polytopes dates from the same period; the book ends with a brief discussion of this conjecture and some of its relations to the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. However, the recent proofs that McMullen's conditions are both sufficient (L. J. Billera and C. W. Lee, 1980) and necessary (R. P. Stanley, 1980) go beyond the scope of the book. Prerequisites for reading the book are modest: standard linear algebra and elementary point set topology in [R1d will suffice Mathematics Combinatorics Mathematik Konvexe Menge (DE-588)4165212-5 gnd rswk-swf Konvexes Polytop (DE-588)4367579-7 gnd rswk-swf Konvexer Körper (DE-588)4165214-9 gnd rswk-swf Konvexes Polytop (DE-588)4367579-7 s 1\p DE-604 Konvexe Menge (DE-588)4165212-5 s 2\p DE-604 Konvexer Körper (DE-588)4165214-9 s 3\p DE-604 https://doi.org/10.1007/978-1-4612-1148-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Brøndsted, Arne An Introduction to Convex Polytopes Mathematics Combinatorics Mathematik Konvexe Menge (DE-588)4165212-5 gnd Konvexes Polytop (DE-588)4367579-7 gnd Konvexer Körper (DE-588)4165214-9 gnd |
| subject_GND | (DE-588)4165212-5 (DE-588)4367579-7 (DE-588)4165214-9 |
| title | An Introduction to Convex Polytopes |
| title_auth | An Introduction to Convex Polytopes |
| title_exact_search | An Introduction to Convex Polytopes |
| title_full | An Introduction to Convex Polytopes by Arne Brøndsted |
| title_fullStr | An Introduction to Convex Polytopes by Arne Brøndsted |
| title_full_unstemmed | An Introduction to Convex Polytopes by Arne Brøndsted |
| title_short | An Introduction to Convex Polytopes |
| title_sort | an introduction to convex polytopes |
| topic | Mathematics Combinatorics Mathematik Konvexe Menge (DE-588)4165212-5 gnd Konvexes Polytop (DE-588)4367579-7 gnd Konvexer Körper (DE-588)4165214-9 gnd |
| topic_facet | Mathematics Combinatorics Mathematik Konvexe Menge Konvexes Polytop Konvexer Körper |
| url | https://doi.org/10.1007/978-1-4612-1148-8 |
| work_keys_str_mv | AT brøndstedarne anintroductiontoconvexpolytopes |