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Unimodal, log-concave and Pólya frequency sequences in combinatorics / / Francesco Brenti
| Unimodal, log-concave and Pólya frequency sequences in combinatorics / / Francesco Brenti |
| Autore | Brenti Francesco <1960-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1989 |
| Descrizione fisica | 1 online resource (118 p.) |
| Disciplina | 511/.6 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Combinatorial analysis
Sequences (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0836-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Foreword""; ""Introduction""; ""Chapter 1 The Poset Conjecture""; ""1.1 Introduction""; ""1.2 Statement of the Poset Conjecture""; ""1.3 Partial results on the Poset Conjecture""; ""1.4 A second look at the Poset Conjecture""; ""Chapter 2 A General Theory""; ""2.1 Introduction""; ""2.2 Polynomials with only real zeros and total positivity""; ""2.3 The six fundamental bases and the transition matrices between them""; ""2.4 Linear transformations that preserve the PF property""; ""2.5 Linear transformations that preserve the PF[sub(2)] property""
""2.6 Summary of results and open problems""""Chapter 3 Ramifications of the General Theory""; ""3.1 Introduction""; ""3.2 Further properties of the six fundamental bases""; ""3.3 The special case of polynomials with no constant term""; ""3.4 Eulerian, Lagrange, and Krawtchouk polynomials""; ""3.5 Three general problems""; ""Chapter 4 Polynomials in PF[([sup(x+d-i)][sub(d)])]""; ""4.1 Introduction""; ""4.2 Elementary properties of PF[([sup(x+d-i)][sub(d)])]""; ""4.3 A Fundamental Theorem""; ""4.4 Consequences of the Fundamental Theorem""; ""4.5 The characterization of PF-sequences"" ""4.6 The characterization of PF[([sup(x+d-i)][sub(d)])]""""4.7 Products of polynomials in PF[([sup(x+d-i)][sub(d)])]""; ""Chapter 5 Applications to the Poset Conjecture""; ""5.1 Introduction""; ""5.2 Ferrers posets""; ""5.3 Column strict labeled Ferrers posets and the solution of a conjecture""; ""5.4 A class of naturally labeled Ferrers posets""; ""5.5 Disjoint unions of chains""; ""5.6 Gaussian posets""; ""5.7 Necessary and sufficient conditions for the Poset Conjecture""; ""Chapter 6 Applications to Enumerative Combinatorics""; ""6.1 Introduction"" ""6.2 PF sequences arising from symmetric functions and Jack polynomials""""6.3 Zeta polynomials of partially ordered sets""; ""6.4 Functions of a finite set into itself""; ""6.5 Associated Lah numbers""; ""6.6 Stirling permutations""; ""6.7 Associated Stirling numbers""; ""6.8 Colorings of graphs""; ""Chapter 7 Polya Frequency Digraphs""; ""7.1 Introduction""; ""7.2 PF digraphs and the distributive lattice conjecture""; ""7.3 A general result""; ""7.4 The connection with the theory of symmetric functions""; ""7.5 The inversion Theorem""; ""7.6 PF[sub(2)] digraphs"" ""7.7 Semitransitive digraphs""""Bibliography""; ""Appendix""; ""Tables"" |
| Record Nr. | UNINA-9910480334803321 |
Brenti Francesco <1960->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1989 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Unimodal, log-concave and Pólya frequency sequences in combinatorics / / Francesco Brenti
| Unimodal, log-concave and Pólya frequency sequences in combinatorics / / Francesco Brenti |
| Autore | Brenti Francesco <1960-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1989 |
| Descrizione fisica | 1 online resource (118 p.) |
| Disciplina | 511/.6 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Combinatorial analysis
Sequences (Mathematics) |
| ISBN | 1-4704-0836-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Foreword""; ""Introduction""; ""Chapter 1 The Poset Conjecture""; ""1.1 Introduction""; ""1.2 Statement of the Poset Conjecture""; ""1.3 Partial results on the Poset Conjecture""; ""1.4 A second look at the Poset Conjecture""; ""Chapter 2 A General Theory""; ""2.1 Introduction""; ""2.2 Polynomials with only real zeros and total positivity""; ""2.3 The six fundamental bases and the transition matrices between them""; ""2.4 Linear transformations that preserve the PF property""; ""2.5 Linear transformations that preserve the PF[sub(2)] property""
""2.6 Summary of results and open problems""""Chapter 3 Ramifications of the General Theory""; ""3.1 Introduction""; ""3.2 Further properties of the six fundamental bases""; ""3.3 The special case of polynomials with no constant term""; ""3.4 Eulerian, Lagrange, and Krawtchouk polynomials""; ""3.5 Three general problems""; ""Chapter 4 Polynomials in PF[([sup(x+d-i)][sub(d)])]""; ""4.1 Introduction""; ""4.2 Elementary properties of PF[([sup(x+d-i)][sub(d)])]""; ""4.3 A Fundamental Theorem""; ""4.4 Consequences of the Fundamental Theorem""; ""4.5 The characterization of PF-sequences"" ""4.6 The characterization of PF[([sup(x+d-i)][sub(d)])]""""4.7 Products of polynomials in PF[([sup(x+d-i)][sub(d)])]""; ""Chapter 5 Applications to the Poset Conjecture""; ""5.1 Introduction""; ""5.2 Ferrers posets""; ""5.3 Column strict labeled Ferrers posets and the solution of a conjecture""; ""5.4 A class of naturally labeled Ferrers posets""; ""5.5 Disjoint unions of chains""; ""5.6 Gaussian posets""; ""5.7 Necessary and sufficient conditions for the Poset Conjecture""; ""Chapter 6 Applications to Enumerative Combinatorics""; ""6.1 Introduction"" ""6.2 PF sequences arising from symmetric functions and Jack polynomials""""6.3 Zeta polynomials of partially ordered sets""; ""6.4 Functions of a finite set into itself""; ""6.5 Associated Lah numbers""; ""6.6 Stirling permutations""; ""6.7 Associated Stirling numbers""; ""6.8 Colorings of graphs""; ""Chapter 7 Polya Frequency Digraphs""; ""7.1 Introduction""; ""7.2 PF digraphs and the distributive lattice conjecture""; ""7.3 A general result""; ""7.4 The connection with the theory of symmetric functions""; ""7.5 The inversion Theorem""; ""7.6 PF[sub(2)] digraphs"" ""7.7 Semitransitive digraphs""""Bibliography""; ""Appendix""; ""Tables"" |
| Record Nr. | UNINA-9910788872503321 |
|
Brenti Francesco <1960->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1989 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Unimodal, log-concave and Pólya frequency sequences in combinatorics / / Francesco Brenti
| Unimodal, log-concave and Pólya frequency sequences in combinatorics / / Francesco Brenti |
| Autore | Brenti Francesco <1960-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1989 |
| Descrizione fisica | 1 online resource (118 p.) |
| Disciplina | 511/.6 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Combinatorial analysis
Sequences (Mathematics) |
| ISBN | 1-4704-0836-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Foreword""; ""Introduction""; ""Chapter 1 The Poset Conjecture""; ""1.1 Introduction""; ""1.2 Statement of the Poset Conjecture""; ""1.3 Partial results on the Poset Conjecture""; ""1.4 A second look at the Poset Conjecture""; ""Chapter 2 A General Theory""; ""2.1 Introduction""; ""2.2 Polynomials with only real zeros and total positivity""; ""2.3 The six fundamental bases and the transition matrices between them""; ""2.4 Linear transformations that preserve the PF property""; ""2.5 Linear transformations that preserve the PF[sub(2)] property""
""2.6 Summary of results and open problems""""Chapter 3 Ramifications of the General Theory""; ""3.1 Introduction""; ""3.2 Further properties of the six fundamental bases""; ""3.3 The special case of polynomials with no constant term""; ""3.4 Eulerian, Lagrange, and Krawtchouk polynomials""; ""3.5 Three general problems""; ""Chapter 4 Polynomials in PF[([sup(x+d-i)][sub(d)])]""; ""4.1 Introduction""; ""4.2 Elementary properties of PF[([sup(x+d-i)][sub(d)])]""; ""4.3 A Fundamental Theorem""; ""4.4 Consequences of the Fundamental Theorem""; ""4.5 The characterization of PF-sequences"" ""4.6 The characterization of PF[([sup(x+d-i)][sub(d)])]""""4.7 Products of polynomials in PF[([sup(x+d-i)][sub(d)])]""; ""Chapter 5 Applications to the Poset Conjecture""; ""5.1 Introduction""; ""5.2 Ferrers posets""; ""5.3 Column strict labeled Ferrers posets and the solution of a conjecture""; ""5.4 A class of naturally labeled Ferrers posets""; ""5.5 Disjoint unions of chains""; ""5.6 Gaussian posets""; ""5.7 Necessary and sufficient conditions for the Poset Conjecture""; ""Chapter 6 Applications to Enumerative Combinatorics""; ""6.1 Introduction"" ""6.2 PF sequences arising from symmetric functions and Jack polynomials""""6.3 Zeta polynomials of partially ordered sets""; ""6.4 Functions of a finite set into itself""; ""6.5 Associated Lah numbers""; ""6.6 Stirling permutations""; ""6.7 Associated Stirling numbers""; ""6.8 Colorings of graphs""; ""Chapter 7 Polya Frequency Digraphs""; ""7.1 Introduction""; ""7.2 PF digraphs and the distributive lattice conjecture""; ""7.3 A general result""; ""7.4 The connection with the theory of symmetric functions""; ""7.5 The inversion Theorem""; ""7.6 PF[sub(2)] digraphs"" ""7.7 Semitransitive digraphs""""Bibliography""; ""Appendix""; ""Tables"" |
| Record Nr. | UNINA-9910828759003321 |
|
Brenti Francesco <1960->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1989 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
