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In April of 1996 an array of mathematicians converged on Cambridge, Massachusetts, for the Rotafest and Umbral Calculus Workshop, two con ferences celebrating Gian-Carlo Rota's 64th birthday. It seemed appropriate when feting one of the world's great combinatorialists to have the anniversary be a power of 2 rather than the more mundane 65. The over seventy-five par ticipants included Rota's doctoral students, coauthors, and other colleagues from more than a dozen countries. As a further testament to the breadth and depth of his influence, the lectures ranged over a wide variety of topics from invariant theory to algebraic topology. This volume is a collection of articles written in Rota's honor. Some of them were presented at the Rotafest and Umbral Workshop while others were written especially for this Festschrift. We will say a little about each paper and point out how they are connected with the mathematical contributions of Rota himself.
List of contents
MacMahon's Partition Analysis: I. The Lecture Hall Partition Theorem.- The cd-Index of Zonotopes and Arrangements.- Letter-Place Methods and Homotopy.- Classification of Trivectors in 6-D Space.- Parameter Augmentation for Basic Hypergeometric Series, I.- Unities and Negation.- The Would-Be Method of Targeted Rings.- Lattice Walks and Primary Decomposition.- Natural Exponential Families and Umbral Calculus.- Umbral Calculus in Hilbert Space.- A Strategy for Determining Polynomial Orthogonality.- Plethystic Formulas and Positivity for q, t-Kostka Coefficients.- An Alternative Evaluation of the Andrews-Burge Determinant.- The Number of Points in a Combinatorial Geometry with No 8-Point-Line Minors.- Umbral Shifts and Symmetric Functions of Schur Type.- An Axiomization for Cubic Algebras.- An Elementary Proof of Roichman's Rule for Irreducible Characters of Iwahori-Hecke Algebras of Type A.- Universal Constructions in Umbral Calculus.- Hyperplane Arrangements, Parking Functions and Tree Inversions.- More Orthogonal Polynomials as Moments.- Difference Equations via the Classical Umbral Calculus.- An Analogy in Geometric Homology: Rigidity and Cofactors on Geometric Graphs.- The Umbral Calculus and Identities for Hypergeometric Functions with Special Arguments.- Apologies to T.S. Eliot: The Rota Nerds.
