The Andrews Festschrift: Seventeen Papers on Classical Number Theory and Combinatorics (English and French Edition)

This book contains seventeen contributions made to George Andrews on the occasion of his sixtieth birthday, ranging from classical number theory (the theory of partitions) to classical and algebraic combinatorics. Most of the papers were read at the 42nd session of the Séminaire Lotharingien de Combinatoire that took place at Maratea, Basilicata, in August 1998. This volume contains a long memoir on Ramanujan's Unpublished Manuscript and the Tau functions studied with a contemporary eye, together with several papers dealing with the theory of partitions. There is also a description of a maple package to deal with general q-calculus. More subjects on algebraic combinatorics are developed, especially the theory of Kostka polynomials, the ice square model, the combinatorial theory of classical numbers, a new approach to determinant calculus. This volume contains the scientific contributions that old friends, colleagues, admirers, former students have made to George Andrews on the occasion of his sixtieth seventeen papers ranging from Classical Number Theory (the theory of partitions dear to George Andrews) to Classical and Algebraic Combinatorics. Most of the papers were read at the 42-nd session of the Seminaire Lotharingien de Combinatoire that took place at Maratea, Basilicata, from August 31 to September 6. 1998. The meeting was made possible thanks to the financial support of the Regione Basilicata and the dipartimento di Matematica, Universita degli Studi della Basilicata and was organized by our colleagues from Potenza, Domenico Senato, Elvira Di Nardo and Paolo Vitolo. We are most thankful to George Andrews for his original paper in which he describes how several great mathematicians, dead or living, have influenced his mathematical career. The second paper could only have been written by his good friend, Richard Askey, who appears to be. in Doron Zeilberger's inimitable language, the "guru" of special functions, George himself being the "q-guru"! Richard very convincingly explains how the year that George spent at Madison in 1975-76 was decisive for them both. There is no better homage to George and his familiarity with Ramanujan's works than this long memoir by Bruce C. Berndt and Ken Ono on Ramanujan's Unpublished Manuscript and the Tau Functions. Bruce has spent a great part of his career deciphering the manuscripts of the great Indian number theorist. Front Matter....Pages i-x Some Debts I Owe....Pages 1-16 The Work of George Andrews: A Madison Perspective....Pages 17-38 Ramanujan’s Unpublished Manuscript on the Partition and Tau Functions with Proofs and Commentary....Pages 39-110 A q -product Tutorial for a q -series Maple Package....Pages 111-138 Un autre q -analogue des nombres d’Euler....Pages 139-158 Three Classical Results on Representations of a Number....Pages 159-165 Simultaneous maj Statistics....Pages 167-178 An Extension of Franklin’s Bijection....Pages 179-187 MacMahon’s Partition Analysis IV: Hypergeometric Multisums....Pages 189-208 Various Representations of the Generalized Kostka Polynomials....Pages 209-226 The Number-Theoretic Content of the Jacobi Triple Product Identity....Pages 227-229 Words and Repeated Factors....Pages 231-251 Explicit Plethystic Formulas for Macdonald q,t-Kostka Coefficients....Pages 253-297 Supernomial Coefficients, Bailey’s Lemma and Rogers—Ramanujan-type Identities....Pages 299-321 The Triple, Quintuple and Septuple Product Identities Revisited....Pages 323-334 Square-Ice Enumeration....Pages 335-348 Advanced Determinant Calculus....Pages 349-426

this Book Contains Seventeen Contributions Made To George Andrews On The Occasion Of His Sixtieth Birthday, Ranging From Classical Number Theory (the Theory Of Partitions) To Classical And Algebraic Combinatorics. Most Of The Papers Were Read At The 42nd Session Of The Séminaire Lotharingien De Combinatoire That Took Place At Maratea, Basilicata, In August 1998.
this Volume Contains A Long Memoir On Ramanujan's Unpublished Manuscript And The Tau Functions Studied With A Contemporary Eye, Together With Several Papers Dealing With The Theory Of Partitions. There Is Also A Description Of A Maple Package To Deal With General Q-calculus. More Subjects On Algebraic Combinatorics Are Developed, Especially The Theory Of Kostka Polynomials, The Ice Square Model, The Combinatorial Theory Of Classical Numbers, A New Approach To Determinant Calculus.