Algebraic Combinatorics and Computer Science

1. Front Matter

   Pages I-X

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2. Introduction

   1. Front Matter

      Pages 1-1

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   2. Ten abandoned gold mines

      • H. Crapo

      Pages 3-22

3. The Fubini Lectures

   1. Front Matter

      Pages 23-23

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   2. Foreword

      • E. Vesentini

      Pages 25-26

   3. The adventures of measure theory

      • G.-C. Rota

      Pages 27-39

   4. What is invariant theory, really?

      • G.-C. Rota

      Pages 41-56

   5. Twelve problems in probability no one likes to bring up

      • G.-C. Rota

      Pages 57-93

4. Recurrent Themes of Gian-Carlo Rota’s Mathematical Thought

   1. Front Matter

      Pages 95-95

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   2. Resolution of Weyl modules: the Rota touch

      • D. A. Buchsbaum

      Pages 97-109

   3. Circulant recursive matrices

      • M. Barnabei, L. B. Montefusco

      Pages 111-127

   4. Remarks on invariant geometric calculus. Cayley-Grassmann algebras and geometric Clifford algebras

      • P. Bravi, A. Brini

      Pages 129-150

   5. Grassmann geometric calculus, invariant theory and superalgebras

      • A. Brini, F. Regonati, A. G. B. Teolis

      Pages 151-196

   6. Rota-Metropolis cubic logic and Ulam-Rényi games

      • F. Cicalese, D. Mundici, U. Vaccaro

      Pages 197-244

   7. Umbral nature of the Poisson random variables

      • E. Di Nardo, D. Senato

      Pages 245-266

   8. A formal theory of resultants (I): an algorithm in invariant theory

      • G.-C. Rota, J. A. Stein

      Pages 267-314

   9. A formal theory of resultants (II): a constructive definition of the resultant

      • G.-C. Rota, J. A. Stein

      Pages 315-342

5. Focus on Catalan Numbers and Combinatorics on Words

   1. Front Matter

      Pages 343-343

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   2. Foreword to the surveys by Aigner and Perrin

      • M. Bamabei, F. Bonetti

      Pages 345-345

   3. Catalan and other numbers: a recurrent theme

      • M. Aigner

      Pages 347-390

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.

• Algebraic Combinatorics
• Alphabet
• Combinatorics
• Computer
• Gian-Carlo Rota
• Graph
• Invariant Theory
• Resolution
• Theoretical Computer Science
• Umbral Calculus
• Variable
• algorithms
• calculus
• combinatorics on words
• logic

• Centre d’Analyse et Mathematique Sociales, E.H.E.S.S. — C.N.R.S., Paris, France

  H. Crapo

• Dipartimento di Matematica, Università della Basilicata, Potenza, Italy

  D. Senato

Policies and ethics