Progress in Mathematics

By: Bruce Sagan, Richard Stanley, Gian-Carlo Rota

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Hardcover | 1 May 1998

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484 Pages

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24.13 x 15.88 x 2.54

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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.

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Preface
Rotafest Program
MacMahon's Partition Analysis: I. The Lecture Hall Partition Theorem	p. 1
The cd-Index of Zonotopes and Arrangements	p. 23
Letter-Place Methods and Homotopy	p. 41
Classification of Trivectors in 6-D Space	p. 63
Parameter Augmentation for Basic Hypergeometric Series, I	p. 111
Unities and Negation	p. 131
The Would-Be Method of Targeted Rings	p. 157
Lattice Walks and Primary Decomposition	p. 173
Natural Exponential Families and Umbral Calculus	p. 195
Umbral Calculus in Hilbert Space	p. 213
A Strategy for Determining Polynomial Orthogonality	p. 239
Plethystic Formulas and Positivity for q,t-Kostka Coefficients	p. 245
An Alternative Evaluation of the Andrews-Burge Determinant	p. 263
The Number of Points in a Combinatorial Geometry with No 8-Point-Line Minors	p. 271
Umbral Shifts and Symmetric Functions of Schur Type	p. 285
An Axiomization for Cubic Algebras	p. 305
An Elementary Proof of Roichman's Rule for Irreducible Characters of Iwahori-Hecke Algebras of Type A	p. 335
Universal Constructions in Umbral Calculus	p. 343
Hyperplane Arrangements, Parking Functions and Tree Inversions	p. 359
More Orthogonal Polynomials as Moments	p. 377
Difference Equations via the Classical Umbral Calculus	p. 397
An Analogy in Geometric Homology: Rigidity and Cofactors on Geometric Graphs	p. 413
The Umbral Calculus and Identities for Hypergeometric Functions with Special Arguments	p. 439
Apologies to T.S. Eliot: The Rota Nerds	p. 459
Table of Contents provided by Blackwell. All Rights Reserved.

Progress in Mathematics

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