The Andrews Festschrift: Seventeen Papers on Classical Number Theory and Combinatorics

ISBN-13: 9783540414919 / Angielski / Miękka / 2001 / 426 str.

D. Foata; G. N. Han; Dominique Foata

Opis

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 Seminaire 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This volume contains a long memoir on Ramanujan's Unpublished Manuscript and the Tau functions studied with a contemporary eye, together with several papers dealing with the theory of partitions.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."

Spis treści

Dominique Foata, Guo-Niu Han Introduction George E. Andrews Some Debts I Owe Richard Askey The Work of George Andrews: A Madison Perspective Bruce C. Berndt, Ken Ono Ramanujans Unpublished Manuscript on the Partition and Tau Functions with Proofs and Commentary Frank Garvan Qseries maple tutorial: A q-product tutorial for a q-series maple package G.-N. Han, A. Randrianarivony, J. Zeng Un autre q-analogue des nombres dÉuler Michael D. Hirschhorn Three classical results on representations of a number Dongsu Kim, Dennis Stanton Simultaneous maj statistics David P. Little An extension of Franklins Bijection George E. Andrews, Peter Paule MacMahons Partition Analysis IV: Hypergeometric Multisums Anatol N. Kirillov, Anne Schilling, Mark Shimozono Various representations of the generalized Kostka polynomials Herbert S. Wilf The number-theoretic content of the Jacobi triple product identity Arturo Carpi, Aldo de Luca Words and Repeated Factors Adriano Garsia, Mark Haiman, Glenn Tesler Explicit Plethystic Formulas for Macdonald q,t-Kostka Coefficients S. Ole Warnaar Supernomial coefficients, Baileys lemma and Rogers-Ramanujan-type identities. A survey of results and open problems D. Foata, G.-N. Han The triple, quintuple and septuple product identities revisited A. Lascoux Square-ice enumeration Christian Krattenthaler Advanced Determinant Calculus