The Andrews Festschrift Seventeen Papers on Classical Number Theory and Combinatorics

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 S?minaire 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Combinatoire that took place at Maratea, Basilicata, in August 1998.This volume contains a long memoir on Ramanujan's Unpublished Manuscript and the Tau functions studied with a contemporary eye, together with several papers dealing with the theory of partitions.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. TOC:The complete table of contents can be found on the Internet: http://www.springer.de/math/

Some Debts I Owe.- The Work of George Andrews: A Madison Perspective.- Ramanujan’s Unpublished Manuscript on the Partition and Tau Functions with Proofs and Commentary.- A q-product Tutorial for a q-series Maple Package.- Un autre q-analogue des nombres d’Euler.- Three Classical Results on Representations of a Number.- Simultaneous maj Statistics.- An Extension of Franklin’s Bijection.- MacMahon’s Partition Analysis IV: Hypergeometric Multisums.- Various Representations of the Generalized Kostka Polynomials.- The Number- Theoretic Content of the Jacobi Triple Product Identity.- Words and Repeated Factors.- Explicit Plethystic Formulas for Macdonald q,t-Kostka Coefficients.- Supernomial Coefficients, Bailey’s Lemma and Rogers-Ramanujan-type Identities. A Survey of Results and Open Problems.- The Triple, Quintuple and Septuple Product Identities Revisited.- Square-Ice Enumeration.- Advanced Determinant Calculus.