Combinatorics and algebra
著者
書誌事項
Combinatorics and algebra
（Contemporary mathematics, v. 34）
American Mathematical Society, c1984
- : pbk
大学図書館所蔵 件 / 全51件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
"Proceedings of the AMS-NSF Joint Summer Research Conference in the Mathematical Sciences on Combinatorics and Algebra, held at the University of Colorado, Boulder, during June 5-11, 1983"--Introd
Includes bibliographies
内容説明・目次
内容説明
This volume contains the Proceedings of the AMS-NSF Joint Summer Research Conference on Combinatorics and Algebra held at the University of Colorado during June 1983. Although combinatorial techniques have pervaded the study of algebra throughout its history, it is only in recent years that any kind of systematic attempt has been made to understand the connections between algebra and combinatorics. This Conference drew together specialists in both and provided an invaluable opportunity for them to collaborate. The topic most discussed was representation theory of the symmetric group and complex general linear group. The close connections with combinatorics, especially the theory of Young tableaux, was evident from the pioneering work of G. Frobenius, I. Schur, A. Young, H. Weyl, and D. E. Littlewood.Phil Hanlon gave an introductory survey of this subject, whose inclusion in this volume should make many of the remaining papers more accessible to a reader with little background in representation theory. Ten of the papers impinge on representation theory in various ways. Some are directly concerned with the groups, Lie algebras, etc., themselves, while others deal with purely combinatorial topics which arose from representation theory and suggest the possibility of a deeper connection between the combinatorics and the algebra.
The remaining papers are concerned with a wide variety of topics. There are valuable surveys on the classical subject of hyperplane arrangements and its recently discovered connections with lattice theory and differential forms, and on the surprising connections between algebra, topology, and the counting of faces of convex polytopes and related complexes.There also appears an instructive example of the interplay between combinatorial and algebraic properties of finite lattices, and an interesting illustration of combinatorial reasoning to prove a fundamental algebraic identity. In addition, a highly successful problem session was held during the conference; a list of the problems presented appears at the end of the volume.
目次
An introduction to the complex representations of the symmetric group and general linear Lie algebra by P. Hanlon The cyclotomic identity by N. Metropolis and G. C. Rota Arrangements of hyperplanes and differential forms by P. Orlik, L. Solomon, and H. Terao Double centralizing theorems for wreath product by A. Regev On the construction of the maximal weight vectors in the tensor algebra of $\mathrm{gl}_n(\mathbb{C})$ by P. Hanlon The q-Dyson conjecture, generalized exponents, and the internal product of Schur functions by R. P. Stanley Spherical designs and group representations by E. Bannai Algorithms for plethysm by Y. M. Chen, A. M. Garsia, and J. Remmel Combinatorial correspondences for Young tableaux, and maximal chains in the weak Bruhat order of $S_n$ by P. Edelman and C. Greene Constructions on rim hook tableaux by D. E. White Orderings of Coxeter groups by A. Bjorner Modularly complemented lattices and shellability by D. Stanton and M. Wachs Counting faces and chains in polytopes and posets by M. M. Bayer and L. J. Billera The combinatorics of $(k,l)$-hook Schur functions by J. B. Remmel Multipartite P-partitions and inner products of skew Schur functions by I. M. Gessel Problem session.
「Nielsen BookData」 より
