Algebraic Combinatorics and Computer Science: A Tribute to Gian-Carlo Rota / Edition 1

by H. Crapo, D. Senato

Overview

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.

Product Details

ISBN-13:	9788847000780
Publisher:	Springer Milan
Publication date:	03/01/2001
Edition description:	2001
Pages:	546
Product dimensions:	6.10(w) x 9.25(h) x 0.05(d)

Table of Contents

Ten abandoned gold mines.- The Fubini Lectures.- Foreword.- The adventures of measure theory.- What is invariant theory, really?.- Twelve problems in probability no one likes to bring up.- Recurrent Themes of Gian-Carlo Rota’s Mathematical Thought.- Resolution of Weyl modules: the Rota touch.- Circulant recursive matrices.- Remarks on Invariant geometric calculus. Cayley-Grassmann algebras and geometric Clifford algebras.- Grassmann geometric calculus, invariant theory and superalgebras.- Rota-Metropolis cubic logic and Ulam-Rényi games.- Umbral nature of the Poisson random variables.- A formal theory of resultants (I): an algorithm in invariant theory.- A formal theory of resultants (II): a constructive definition of the resultant.- Focus on Catalan Numbers and Combinatorics on Words.- Foreword to the surveys by Aigner and Perrin.- Catalan and other numbers: a recurrent theme.- Enumerative combinatorics on words.- Algebraic Combinatorics and Theoretical Computer Science.- Alphabet splitting.- Some operations on the family of equivalence relations.- Solving linear recurrences using functionals.- Polynomiality of the q, t-Kostka revisited.- A combinatorial approach to the theory of Pi-algebras and exponential growth.- On the permanent of certain circulant matrices.- Episturmian words and morphisms (results and conjectures).- A curious characteristic property of standard Sturmian words.

Editorial Reviews

This tribute to Rota by 31 contributors from Europe and North America opens with "Ten Abandoned Gold Mines," wherein Crapo (mathematics, Universit<`a> della Basilicata) delimits areas of research Rota began—areas such as sample spaces, entropy as a lattice concept, intrinsic volumes, and invariant theory and superalgebra—but now are being developed by others. Rota's 1998 Fubini Lectures on measure and invariant theories, and his 12 probability problems follow, and eight articles on recurrent themes in Rota's thinking discuss such topics as the umbral nature of the Poisson random variables, circulant recursive matrices, and resolution of Weyl modules. Two articles take up the Catalan Numbers and the generation of series for formal languages and rational series. The last eight contributions address important areas of research (Sturmian words and circulant matrices) in algebraic combinatorics and theoretical computer science, both areas heavily influenced by Rota. The volume is not indexed. Annotation c. Book News, Inc., Portland, OR