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This volume contains a long memoir on Ramanujan's Unpublished Manuscript and the Tau functions studied with a contemporary eye, together with several papers dealing with the theory of partitions.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This volume contains a long memoir on Ramanujan's Unpublished Manuscript and the Tau functions studied with a contemporary eye, together with several papers dealing with the theory of partitions.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

---

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This volume contains a long memoir on Ramanujan's Unpublished Manuscript and the Tau functions studied with a contemporary eye, together with several papers dealing with the theory of partitions.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