Algebraic Combinatorics and Computer Science

by H. Crapo (Editor), D. Senato

Synopsis of Algebraic Combinatorics and Computer Science

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.

Booknews

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

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