Rationality and Reciprocity for the Greedy Normal Form of a Coxeter Group
نویسنده
چکیده
We show that the characteristic series for the greedy normal form of a Coxeter group is always a rational series and prove a reciprocity formula for this series when the group is right-angled and the nerve is Eulerian. As corollaries we obtain many of the known rationality and reciprocity results for the growth series of Coxeter groups as well as some new ones.
منابع مشابه
The Greedy Algorithm and Coxeter Matroids
The notion of matroid has been generalized to Coxeter matroid by Gelfand and Serganova. To each pair (W, P) consisting of a finite irreducible Coxeter group W and parabolic subgroup P is associated a collection of objects called Coxeter matroids. The (ordinary) matroids are a special case, the case W = An (isomorphic to the symmetric group Symn+1) and P a maximal parabolic subgroup. The main re...
متن کاملGarside Families in Artin–tits Monoids and Low Elements in Coxeter Groups
where both terms consist of two alternating letters and have the same length. First investigated by J.Tits in the late 1960s [2], and then in [3] and [11], these groups remain incompletely understood, with many open questions, including the decidability of the Word Problem in the general case [6]. The only well understood case is the one of spherical type, which is the case when the associated ...
متن کاملLogspace computations in Coxeter groups and graph groups
Computing normal forms in groups (or monoids) is computationally harder than solving the word problem (equality testing), in general. However, normal form computation has a much wider range of applications. It is therefore interesting to investigate the complexity of computing normal forms for important classes of groups. For Coxeter groups we show that the following algorithmic tasks can be so...
متن کاملThe Greedy Flip Tree of a Subword Complex
We describe a canonical spanning tree of the ridge graph of a subword complex on a finite Coxeter group. It is based on properties of greedy facets in subword complexes, defined and studied in this paper. Searching this tree yields an enumeration scheme for the facets of the subword complex. This algorithm extends the greedy flip algorithm for pointed pseudotriangulations of points or convex bo...
متن کاملLogspace Computations in Graph Groups and Coxeter Groups
Computing normal forms in groups (or monoids) is in general harder than solving the word problem (equality testing). However, normal form computation has a much wider range of applications. It is therefore interesting to investigate the complexity of computing normal forms for important classes of groups. We show that shortlex normal forms in graph groups and in right-angled Coxeter groups can ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008