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Algebraic Combinatorics and Computer Science : A Tribute to Gian-Carlo Rota - Henry H. Crapo

Algebraic Combinatorics and Computer Science

A Tribute to Gian-Carlo Rota

By: Henry H. Crapo (Editor), D. Senato (Editor)

Hardcover Published: 1st January 2001
ISBN: 9788847000780
Number Of Pages: 546

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This book, dedicated to the memory of Gian-Carlo Rota, is the result of a collaborative effort by his friends, students and admirers. Rota was one of the great thinkers of our times, innovator in both mathematics and phenomenology. I feel moved, yet touched by a sense of sadness, in presenting this volume of work, despite the fear that I may be unworthy of the task that befalls me. Rota, both the scientist and the man, was marked by a generosity that knew no bounds. His ideas opened wide the horizons of fields of research, permitting an astonishing number of students from all over the globe to become enthusiastically involved. The contagious energy with which he demonstrated his tremendous mental capacity always proved fresh and inspiring. Beyond his renown as gifted scientist, what was particularly striking in Gian-Carlo Rota was his ability to appreciate the diverse intellectual capacities of those before him and to adapt his communications accordingly. This human sense, complemented by his acute appreciation of the importance of the individual, acted as a catalyst in bringing forth the very best in each one of his students. Whosoever was fortunate enough to enjoy Gian-Carlo Rota's longstanding friendship was most enriched by the experience, both mathematically and philosophically, and had occasion to appreciate son cote de bon vivant. The book opens with a heartfelt piece by Henry Crapo in which he meticulously pieces together what Gian-Carlo Rota's untimely demise has bequeathed to science.

Introduction
Ten abandoned gold minesp. 3
The Fubini Lectures
Forewordp. 25
The adventures of measure theoryp. 27
What is invariant theory, really?p. 41
Twelve problems in probability no one likes to bring upp. 57
Recurrent Themes of Gian-Carlo Rota's Mathematical Thought
Resolution of Weyl modules: the Rota touchp. 97
Circulant recursive matricesp. 111
Remarks on Invariant geometric calculus. Cayley-Grassmann algebras and geometric Clifford algebrasp. 129
Grassmann geometric calculus, invariant theory and superalgebrasp. 151
Rota-Metropolis cubic logic and Ulam-Renyi gamesp. 197
Umbral nature of the Poisson random variablesp. 245
A formal theory of resultants (I): an algorithm in invariant theoryp. 267
A formal theory of resultants (II): a constructive definition of the resultantp. 315
Focus on Catalan Numbers and Combinatorics on Words
Foreword to the surveys by Aigner and Perrinp. 345
Catalan and other numbers: a recurrent themep. 347
Enumerative combinatorics on wordsp. 391
Algebraic Combinatorics and Theoretical Computer Science
Alphabet splittingp. 431
Some operations on the family of equivalence relationsp. 445
Solving linear recurrences using functionalsp. 461
Polynomiality of the q, t-Kostka revisitedp. 473
A combinatorial approach to the theory of PI-algebras and exponential growthp. 493
On the permanent of certain circulant matricesp. 513
Episturmian words and morphisms (results and conjectures)p. 533
A curious characteristic property of standard Sturmian wordsp. 541
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9788847000780
ISBN-10: 8847000785
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 546
Published: 1st January 2001
Publisher: Springer Verlag
Country of Publication: IT
Dimensions (cm): 23.5 x 16.51  x 1.91
Weight (kg): 0.95