The Bruhat order on the involutions of the hyperoctahedral group.
The subject of Coxeter groups and their posets using the Bruhat ordering became an active area of research. Several generalizations were made to the Bruhat order defined on a Coxeter group. Schubert polynomials and their multiplication can be defined right from such posets. This article is a serious attempt to apply a lot of well known results to a specific group, namely the hyperoctahedral group \(B_n\). It is a profound contribution to the subject to show that the graph of the involutions of \(B_n\) is graded, EL-shellable, Cohen-Macaulay, Eulerian and Gorenstein. The author has written the article neatly and explained every single concept that is needed in the sequel. However this article is mostly computational oriented rather than theoretic, although it opens the road to more sophisticated studies in the area.
scientific article; zbMATH DE number 2003949
scientific article