The Symmetric GroupELSEVIERPure and Applied Physics
We shall first recall the definition, two criterions, and some properties of Bruhat order on the symmetric group. Then we give a survey of various appearances of the Bruhat order in the field of Schubert Calculus. 报告人简介: 范久瑜,四川大学数学学院副教授,主要从事 Schubert 计数演算的组合学、...
symmetric grp很有意思,里面可以证明出来很多有意思的结论,但我们还是专注于群论的主线。以后再专门出各个群的细节。
Let Sn be the symmetric group on the set [n]={1,2,⋯,n} and α∈Sn. Then there exist disjoint cycles α1,α2,⋯,αk in Sn, where αi be ri-cycle for i=1,2,⋯,k such that α=α1α2⋯αk, and furthermore the order of α is the least common multiple of r1,r2...
We also discuss the insights provided by BICs in several emerging research frontiers, such as parity–time symmetric systems, higher-order topology, exciton–photon coupling and moiré superlattices. Key points Photonics provides a versatile platform to study and exploit the properties of bound states ...
A new approach to the character theory of the symmetric group has been developed during the past fifteen years which is in many ways more efficient, more transparent, and more elementary. In this approach, to each permutation is assigned a class function of the corresponding symmetric group. Pro...
By use of a notion of constructibility for partially ordered sets, it is proved that the absolute order on the symmetric group is homotopy Cohen-Macaulay. This answers in part a question raised by V. Reiner and M. Wachs. The Euler characteristic of the order complex of the proper part ...
Many of the theorems will be given without proof; for a systematic treatment the reader is referred to the textbooks on the symmetric group (Rutherford,(1) Robinson,(2) Hamermesh,(3) Boerner(4)). Some of these basic notions are presented in a very nice way in the review of Coleman(5...
A block character of a finite symmetric group is a positive definite function which depends only on the number of cycles in a permutation. We describe the cone of block characters by identifying its extreme rays, and find relations of the characters to descent representations and the coinvariant...
The simple groupFH(8, 2) of order 212· 35· 52· 7 and the associated geometry of triality Proc. London Math Soc., 18 (1968), pp. 521-562 (3) Crossref View in Scopus Google Scholar 5. R.H Dye Symmetric groups as maximal subgroups of orthogonal and symplectic groups over the fiel...