Given a finite Coxeter system (W,S) and a Coxeter element c, or equivalently an orientation of the Coxeter graph of W , we construct a simple polytope whose outer normal fan is N. Reading’s Cambrian fan Fc, settling a conjecture of Reading that this is possible. We call this polytope the c-generalized associahedron. Our approach generalizes Loday’s realization of the associahedron (a type A c-g...

Let (W, S, 0) be a Coxeter system: a Coxeter group W with S its distinguished generator set and 0 its Coxeter graph. In the present paper, we always assume that the cardinality l = |S| of S is finite. A Coxeter element of W is by definition a product of all generators s ∈ S in any fixed order. We use the notation C(W ) to denote the set of all the Coxeter elements in W . These elements play an ...

the concept of comprehensive grobner bases was introduced by weispfenning. montes has proposed an efficient algorithm for computing these bases. but he has not explicitly used buchberger's criteria in his algorithm. in this paper we prove that we can apply these criteria on montes algorithm. we propose a modified version of montes algorithm and evaluate its performance via some examples.

The lectin of the tomato, Lycopersicon esculentum, or of the potato, Solanum tuberosum, can be passively coupled to amide-modified polystyrene spheres to be used as a detection reagent for the specific identification of group B streptococcal cultures grown in selective or nonselective Todd-Hewitt broth for 5 and 4 h, respectively. Agglutination occurred when the lectin reagents were allowed to ...

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...

In this paper we prove that any irreducible Coxeter group of infinite order is directly indecomposable as an abstract group, without the finite rank assumption. The key ingredient of the proof is that we can determine, for an irreducible Coxeter group W , the centralizers in W of the normal subgroups of W that are generated by involutions. As a consequence, we show that the problem of deciding ...

Noncompact hyperbolic Coxeter n-polytopes of finite volume and having n+ 3 facets are studied in this paper. Unlike the spherical and parabolic cases, no complete classification exists as yet for hyperbolic Coxeter polytopes of finite volume. It has been shown that the dimension of a bounded Coxeter polytope is at most 29 (Vinberg, 1984), while an upper estimate in the unbounded case is 995 (Pr...

Coxeter matroids are combinatorial objects associated with finite Coxeter groups; they can be viewed as subsets M of the factor set W/P of a Coxeter group W by a parabolic subgroup P which satisfy a certain maximality property with respect to a family of shifted Bruhat orders on W/P . The classical matroids of matroid theory are exactly the Coxeter matroids for the symmetric group Symn (which i...

In this paper, we propose a second-order corrector interior-point algorithm for semidefinite programming (SDP). This algorithm is based on the wide neighborhood. The complexity bound is O( √ nL) for the Nesterov-Todd direction, which coincides with the best known complexity results for SDP. To our best knowledge, this is the first wide neighborhood second-order corrector algorithm with the same...