Combinatory Analysis: Dedicated to George Andrews

ISBN-13: 9781461478577 / Angielski / Twarda / 2013 / 472 str.

Krishnaswami Alladi; Peter Paule; James Sellers

Opis

George Andrews is one of the most influential figures in number theory and combinatorics. In the theory of partitions and q-hypergeometric series and in the study of Ramanujan's work, he is the unquestioned leader. To suitably honor him during his 70th birthday year, an International Conference on Combinatory Analysis was held at The Pennsylvania State University during December 5-7, 2008. Three issues of the Ramanujan Journal comprising Volume 23 were published in 2010 as the refereed proceedings of that conference. The Ramanujan Journal was proud to bring out that volume honoring one of its Founding Editors. In view of the great interest that the mathematical community has in the influential work of Andrews, it was decided to republish Volume 23 of The Ramanujan Journal in this book form, so that the refereed proceedings are more readily available for those who do not subscribe to the journal but wish to possess this volume. As a fitting tribute to George Andrews, many speakers from the conference contributed research papers to this volume which deals with a broad range of areas that signify the research interests of George Andrews. In reproducing Volume 23 of The Ramanujan Journal in this book form, we have included two papers-one by Hei-Chi Chan and Shaun Cooper, and another by Ole Warnaar-which were intended for Volume 23 of The Ramanujan Journal, but appeared in other issues. The enormous productivity of George Andrews remains unabated in spite of the passage of time. His immensely fertile mind continues to pour forth seminal ideas year after year. He has two research papers in this volume. May his eternal youthfulness and his magnificent research output continue to inspire and influence researchers in the years ahead.

Spis treści

​Congruences modulo powers of 2 for a certain partition function (H.-C. Chan and S. Cooper).- Cranks—really, the final problem (B.C. Berndt, H.H. Chan, S.H. Chan, and W.-C. Liaw).- Eisenstein series and Ramanujan-type series for 1/π (N.D. Baruah and B.C. Berndt).- Parity in partition identities (G.E. Andrews).- Some combinatorial properties of hook lengths, contents, and parts of partitions (R.P. Stanley).- The doubloon polynomial triangle (D. Foata and G.-N. Han).- Hook lengths and shifted parts of partitions (G.-N. Han).- A unification of two refinements of Eluer's partition theorem (W.Y.C. Chen, H.Y. Gao, K.Q. Ji, and M.Y.X. Li).- Identities and congruences for Rajamnujan's ω(q) (J.H. Bruinier and K. Ono).- On the subpartitions of the ordinary partitions (B. Kim).- Arithmetic properties of partitions with even parts distinct (G.E. Andrews, M.D. Hirschhorn, and J.A. Sellers).- Modularity and the distinct rank function (A. Folsom).- Cluster parity indices of partitions (K. Kurşungöz).- Ramanujan's partial theta series and parity in partitions (A.J. Yee).- A combinatorial study and comparison of partial theta identities of Andrews and Ramanujan (K. Alladi).- New identities involving sums of the tails related to real quadratic fields (K. Bringmann and B. Kane).- Rademacher-type formulas for restricted partition and overpartition functions (A.V. Sills).- Bijective proofs using two-line matrix representations for partitions (E.H.M. Brietzke, J.P.O. Santos, and R. da Silva).- Balanced partitions (S. Vandervelde).- Partitions with rounded occurrences and attached parts (J. Lovejoy).- Shifted versions of the Bailey and Well-Poised Bailey lemmas (F. Jouhet).- Column-to-row operations on partitions: Garden of Eden partitions (B. Hopkins and L. Kolitsch).- Some Fine combinatorics (D.P. Little).- Symmetrically constrained compositions (M. Beck, I.M. Gessel, S. Lee, and C.D. Savage).- Bentley's conjecture on popularity toplist turnover under random copying (K. Eriksson, F. Jansson, and J. Sjöstrand).- Log-convexity properties of Schur functions and generalized hypergeometric functions of matrix argument (D.St.P. Richards).- Infinite families of strange partition congruences for broken 2-diamonds (P. Paule and S. Radu).- On the Andrew–Schur proof of the Rogers–Ramanujan identities (H.-C. Chan).- New multiple 6ψ6 summation formulas and related conjectures (V.P. Spiridonov and S.O. Warnaar).

Blurb

George Andrews is one of the most influential figures in number theory and combinatorics. In the theory of partitions and q-hypergeometric series and in the study of Ramanujan's work, he is the unquestioned leader. To suitably honor him during his 70^th birthday year, an international conference on Combinatory Analysis was held at The Pennsylvania State University, December 5–7, 2008. Three issues of The Ramanujan Journal comprising Volume 23 were published in 2010 as the refereed proceedings of that conference. In view of the great interest that the mathematical community has in the influential work of Andrews, it was decided to republish Volume 23 of The Ramanujan Journal in book form, so that the refereed proceedings are more readily available for those who do not subscribe to the journal but wish to possess this volume.

The broad range of areas covered during the conference included the many facets of the theory of partitions, single and multi-variable q-hypergeometric series, various aspects of Ramanujan's mathematics, analytic number theory, and combinatorial number theory—areas which collectively were classified under the heading of Combinatory Analysis by MacMahon and his contemporaries in the early part of the twentieth century. As a fitting tribute to George Andrews, many speakers from the conference contributed research papers to this volume, which deals with a broad range of areas that signify the research interests of George Andrews. In reproducing Volume 23 of The Ramanujan Journal in this book form, we have included two relevant papers that appeared in other issues of the journal.