Mathematical Essays in honor of Gian-Carlo Rota

1. Front Matter

   Pages i-xiii

   PDF

2. MacMahon’s Partition Analysis: I. The Lecture Hall Partition Theorem

   • George E. Andrews

   Pages 1-22

3. The cd-Index of Zonotopes and Arrangements

   • Louis J. Billera, Richard Ehrenborg, Margaret Readdy

   Pages 23-40

4. Letter-Place Methods and Homotopy

   • David A. Buchsbaum

   Pages 41-62

5. Classification of Trivectors in 6-D Space

   • Wendy Chan

   Pages 63-110

6. Parameter Augmentation for Basic Hypergeometric Series, I

   • William Y. C. Chen, Zhi-Guo Liu

   Pages 111-129

7. Unities and Negation

   • Henry Crapo, Claude Le Conte de Poly-Barbut

   Pages 131-155

8. The Would-Be Method of Targeted Rings

   • Ottavio M. D’Antona

   Pages 157-172

9. Lattice Walks and Primary Decomposition

   • Persi Diaconis, David Eisenbud, Bernd Sturmfels

   Pages 173-193

10. Natural Exponential Families and Umbral Calculus

    • A. di Bucchianico, D. E. Loeb

    Pages 195-211

11. Umbral Calculus in Hilbert Space

    • Alessandro di Bucchianico, Daniel E. Loeb, Gian-Carlo Rota

    Pages 213-238

12. A Strategy for Determining Polynomial Orthogonality

    • J. M. Freeman

    Pages 239-244

13. Plethystic Formulas and Positivity for q,t-Kostka Coefficients

    • A. M. Garsia, J. Remmel

    Pages 245-262

14. An Alternative Evaluation of the Andrews-Burge Determinant

    • C. Krattenthaler

    Pages 263-270

15. The Number of Points in a Combinatorial Geometry with No 8-Point-Line Minors

    • Joseph E. Bonin, Joseph P. S. Kung

    Pages 271-284

16. Umbral Shifts and Symmetric Functions of Schur Type

    • Miguel A. Méndez

    Pages 285-303

17. An Axiomization for Cubic Algebras

    • Colin Bailey, Joseph Oliveira

    Pages 305-334

18. An Elementary Proof of Roichman’s Rule for Irreducible Characters of Iwahori-Hecke Algebras of Type A

    • Arun Ram

    Pages 335-342

19. Universal Constructions in Umbral Calculus

    • Nigel Ray

    Pages 343-357

20. Hyperplane Arrangements, Parking Functions and Tree Inversions

    • Richard P. Stanley

    Pages 359-375

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.

• Hilbert space
• Hypergeometric function
• Identity
• Invariant
• Topology
• algebra
• calculus
• classification
• equation
• function
• geometry
• graphs
• orthogonal polynomials
• proof
• theorem
• combinatorics

• Department of Mathematics, Michigan State University, East Lansing, USA

  Bruce E. Sagan

• Department of Mathematics, MIT, Cambridge, USA

  Richard P. Stanley

Policies and ethics