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TitleMathematical Essays in honor of Gian-Carlo Rota [electronic resource] / edited by Bruce E. Sagan, Richard P. Stanley
ImprintBoston, MA : Birkhรคuser Boston, 1998
Connect tohttp://dx.doi.org/10.1007/978-1-4612-4108-9
Descript XIV, 466 p. online resource

SUMMARY

In April of 1996 an array of mathematicians converged on Cambridge, Massachusetts, for the Rotafest and Umbral Calculus Workshop, two conยญ 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 parยญ 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


CONTENT

MacMahonโ{128}{153}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 Roichmanโ{128}{153}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


Mathematics Combinatorics Mathematics Combinatorics



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