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 P F 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 P F 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 PF
2
digraphs 94
7.7 Semitransitive digraphs 97
Bibliography 99
Appendix 103
Tables 104
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