Unimodal, log-concave and Pólya frequency sequences in combinatorics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
1989
|
| Series: | Memoirs of the American Mathematical Society
413 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 81, Number 413 (fourth of 6 numbers) |
| Physical Description: | VIII, 106 S. |
| ISBN: | 0821824767 |
Staff View
MARC
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| 245 | 1 | 0 | |a Unimodal, log-concave and Pólya frequency sequences in combinatorics |c Francesco Brenti |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1989 | |
| 300 | |a VIII, 106 S. | ||
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Record in the Search Index
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| adam_text | Contents
Foreword vi
Introduction vii
Chapter 1 The Poset Conjecture 1
1.1 Introduction 1
1.2 Statement of the Poset Conjecture 1
1.3 Partial results on the Poset Conjecture 4
1.4 A second look at the Poset Conjecture 6
Chapter 2 A General Theory 8
2.1 Introduction 8
2.2 Polynomials with only real zeros and total positivity 8
2.3 The six fundamental bases and the transition matrices
between them 12
2.4 Linear transformations that preserve the PF property 16
2.5 Linear transformations that preserve the PF2 property 21
2.6 Summary of results and open problems 24
Chapter S Ramifications of the General Theory 27
3.1 Introduction 27
3.2 Further properties of the six fundamental bases 27
3.3 The special case of polynomials with no constant term 30
3.4 Eulerian, Lagrange, and Krawtchouk polynomials 31
3.5 Three general problems 35
Chapter 4 Polynomials in Pf[Yx+^~ )1 39
4.1 Introduction 39
4.2 Elementary properties of PF[(x d~ )J 39
4.3 A Fundamental Theorem 41
4.4 Consequences of the Fundamental Theorem 43
4.5 The characterization of PF sequences 44
4.6 The characterization of PF[(i+*~ )] 48
4.7 Products of polynomials in PF^* 1 1* 1)] 50
Chapter 5 Applications to the Poset Conjecture 56
5.1 Introduction 56
5.2 Ferrers posets 56
5.3 Column strict labeled Ferrers posets and the solution of a
conjecture by R. Stanley 59
5.4 A class of naturally labeled Ferrers posets 61
5.5 Disjoint unions of chains 62
5.6 Gaussian posets 63
5.7 Necessary and sufficient conditions for the Poset Conjecture 65
Chapter 6 Applications to Enumerative Combinatorics 68
6.1 Introduction 68
6.2 PF sequences arising from symmetric functions and
Jack polynomials 68
6.3 Zeta polynomials of partially ordered sets 72
6.4 Functions of a finite set into itself 74
6.5 Associated Lah numbers 75
6.6 Stirling permutations 77
6.7 Associated Stirling numbers 81
6.8 Colorings of graphs 82
Chapter 7 Polya Frequency Digraphs 85
7.1 Introduction 85
7.2 PF digraphs and the distributive lattice conjecture 85
7.3 A general result 88
7.4 The connection with the theory of symmetric functions 90
7.5 The inversion Theorem 93
7.6 PF2 digraphs 94
7.7 Semitransitive digraphs 97
Bibliography 99
Appendix 103
Tables 104
|
| any_adam_object | 1 |
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| dewey-search | 510 511/.6 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV002657461 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:48:00Z |
| institution | BVB |
| isbn | 0821824767 |
| language | English |
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| physical | VIII, 106 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Brenti, Francesco 1960- Verfasser (DE-588)17198949X aut Unimodal, log-concave and Pólya frequency sequences in combinatorics Francesco Brenti Providence, RI American Math. Soc. 1989 VIII, 106 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 413 Volume 81, Number 413 (fourth of 6 numbers) Analise Combinatoria larpcal Combinatorial analysis Sequences (Mathematics) Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 s DE-604 Memoirs of the American Mathematical Society 413 (DE-604)BV008000141 413 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001703876&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brenti, Francesco 1960- Unimodal, log-concave and Pólya frequency sequences in combinatorics Memoirs of the American Mathematical Society Analise Combinatoria larpcal Combinatorial analysis Sequences (Mathematics) Kombinatorische Analysis (DE-588)4164746-4 gnd |
| subject_GND | (DE-588)4164746-4 |
| title | Unimodal, log-concave and Pólya frequency sequences in combinatorics |
| title_auth | Unimodal, log-concave and Pólya frequency sequences in combinatorics |
| title_exact_search | Unimodal, log-concave and Pólya frequency sequences in combinatorics |
| title_full | Unimodal, log-concave and Pólya frequency sequences in combinatorics Francesco Brenti |
| title_fullStr | Unimodal, log-concave and Pólya frequency sequences in combinatorics Francesco Brenti |
| title_full_unstemmed | Unimodal, log-concave and Pólya frequency sequences in combinatorics Francesco Brenti |
| title_short | Unimodal, log-concave and Pólya frequency sequences in combinatorics |
| title_sort | unimodal log concave and polya frequency sequences in combinatorics |
| topic | Analise Combinatoria larpcal Combinatorial analysis Sequences (Mathematics) Kombinatorische Analysis (DE-588)4164746-4 gnd |
| topic_facet | Analise Combinatoria Combinatorial analysis Sequences (Mathematics) Kombinatorische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001703876&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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