## Algebraic Combinatorics and Computer Science: A Tribute to Gian-Carlo RotaThis 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. |

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### Contents

Ten abandoned gold mines | 3 |

Foreword | 25 |

The adventures of measure theory | 27 |

What is invariant theory really? | 41 |

Twelve problems in probability no one likes to bring up | 57 |

the Rota touch | 97 |

Circulant recursive matrices | 111 |

Remarks on invariant geometric calculus CayleyGrassmann algebras and geometric Clifford algebras | 129 |

Foreword to the surveys by Aigner and Perrin | 345 |

a recurrent theme | 347 |

Enumerative combinatorics on words | 391 |

Alphabet splitting | 431 |

Some operations on the family of equivalence relations | 445 |

Solving linear recurrences using functionals | 461 |

Polynomiality of the q tKostka revisited | 473 |

A combinatorial approach to the theory of PIalgebras and exponential growth | 493 |

Grassmann geometric calculus invariant theory and superalgebras | 151 |

RotaMetropolis cubic logic and UlamRényi games | 197 |

Umbral nature of the Poisson random variables | 245 |

an algorithm in invariant theory | 267 |

a constructive definition of the resultant | 315 |

On the permanent of certain circulant matrices | 513 |

Episturmian words and morphisms results and conjectures | 533 |

A curious characteristic property of standard Sturmian words | 541 |

### Other editions - View all

Algebraic Combinatorics and Computer Science: A Tribute to Gian-Carlo Rota H. Crapo,D. Senato Limited preview - 2012 |

Algebraic Combinatorics and Computer Science: A Tribute to Gian-Carlo Rota H. Crapo,D. Senato No preview available - 2012 |

### Common terms and phrases

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