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Algebraic Combinatorics and Computer Science

A Tribute to Gian-Carlo Rota

  • Book
  • © 2001

Overview

Editors:
  1. H. Crapo

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

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  2. D. Senato

    1. Dipartimento di Matematica, Università della Basilicata, Potenza, Italy

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  • This tribute to Giancarlo Rota is the result of a unique cooperation of leading researchers in this field, deeply influenced by Rota's thought
  • The essays and research papers deal with the latest developments in maths

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Table of contents (24 chapters)

  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
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Keywords

About this book

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.

Editors and Affiliations

  • 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

Bibliographic Information

  • Book Title: Algebraic Combinatorics and Computer Science

  • Book Subtitle: A Tribute to Gian-Carlo Rota

  • Editors: H. Crapo, D. Senato

  • DOI: https://doi.org/10.1007/978-88-470-2107-5

  • Publisher: Springer Milano

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Italia 2001

  • Hardcover ISBN: 978-88-470-0078-0Published: 01 January 2001

  • Softcover ISBN: 978-88-470-2159-4Published: 06 October 2012

  • eBook ISBN: 978-88-470-2107-5Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: X, 546

  • Topics: Discrete Mathematics, Combinatorics, Computational Mathematics and Numerical Analysis, Theory of Computation

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