Unimodal, log-concave and Pólya frequency sequences in combinatorics / / Francesco Brenti

• Record Nr.: UNINA9910828759003321
• Autore: Brenti Francesco <1960->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 1989; ©1989
• ISBN: 1-4704-0836-8
• Descrizione fisica: 1 online resource (118 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Number 413
• Disciplina: 511/.6
• Soggetti: Combinatorial analysis; Sequences (Mathematics)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "September 1989, Volume 81, Number 413 (fourth of 6 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• 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""