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

ISBN-13: 9788847000780 / Angielski / Twarda / 2001 / 546 str.

D. Senato; H. Crapo; H. Crapo

Opis

The present volume is a tribute to Gian-Carlo Rota. It is an anthology of the production of a unique collaboration among leading researchers who were greatly influenced by Gian-Carlo Rota's mathematical thought.
The book begins with an essay in mathematical biography by H. Crapo in which the prospects for research opened up by Rota's work are outlined. The subsequent section is devoted to the prestigious Fubini lectures delivered by Gian-Carlo Rota at the Institute for scientific Interchange in 1998, with a preface by E. Vesentini. These lectures provide the only published documentation of Rota's plans for a fundamental reform of probability theory, a program interrupted by his untimely demise.
The lectures by M. Aigner and D. Perrin specially conceived for this volume, provide self-contained surveys of central topics in combinatorics and theoretical computer science; they will also be of great use to both undergraduate and graduate students.
The essays and research papers that appear in the final section present recent developments of some of the mathematical themes promoted by Gian-Carlo Rota. These will be of particular interest as they propose many new problems for research.

Spis treści

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.