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