Combinatorial aspects of excedances and the Frobenius complex

COMBINATORIAL ASPECTS OF EXCEDANCES AND THE FROBENIUS COMPLEX
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Abstract
Title Page
Acknowledgments
Dedication
Table of Contents
List of Figures
1 Introduction
1.1 Dissertation results
1.2 Permutations, partitions, and rooks
1.3 Posets
1.4 Coxeter groups
1.5 Juggling
1.6 Topological tools
1.7 Discrete Morse theory
2 Affine excedances
2.1 Introduction
2.2 Coset representatives and increasing juggling patterns
2.3 Affine excedances
2.4 The root polytope
2.5 The skew root polytope
2.6 Enumerating staircases
2.7 Concluding remarks
3 The excedance algebra
3.1 Introduction
3.2 Expansion
3.3 The operators E and
3.4 Gandhi polynomials and Genocchi numbers
3.5 Concluding remarks
4 The Frobenius complex
4.1 Introduction
4.2 Discrete Morse theory
4.3 Generating functions
4.4 Two generators
4.5 Generators in the arithmetic sequence {a,a+d,…,a+(a-1)d}
4.6 Concluding remarks
5 Enumerating Q-factorial posets
5.1 Introduction
5.2 Q-factorial posets
5.3 Computing Rk(Q)
5.4 Concluding remarks
Bibliography
Vita