We give a new proof of Brink’s theorem that the nonreflection part of a reflection centralizer in a Coxeter group is free, and make several refinements. In particular we give an explicit finite set of generators for the centralizer and a method for computing the Coxeter diagram for its reflection part. In many cases, our method allows one to compute centralizers quickly in one’s head. We also d...

A group of isometries a hyperbolic n-space is called reflection if it generated by reflections in hyperplanes. Vinberg gave semi-algorithm for finding maximal sublattice given arithmetic subgroup $${{\,\textrm{O}\,}}(n,1)$$ the simplest type. We provide an effective termination condition Vinberg’s with which becomes algorithm sublattices. The main new ingredient proof upper bound number faces C...

In this paper, we propose a simple variant of the Mizuno-Todd-Ye predictor-corrector algorithm for linear programming problem (LP). Our variants execute a natural finite termination procedure at each iteration and it is easy to implement the algorithm. Our algorithm admits an objective-function free polynomial-time complexity when it is applied to LPs whose dual feasible region is bounded.

The addition of 5 microgram of clindamycin per ml to a modified Todd-Hewitt growth medium permitted the ready enumeration of Eikenella corrodens from deep periodontal lesions because it allowed differential growth amongst the periodontal pocket gram-negative microaerophilic-anaerobic flora, maximized the numbers of E. corrodens in such culture, and inhibited the growth of most of the other conf...

Louis Solomon showed that the group algebra of the symmetric group Sn has a subalgebra called the descent algebra, generated by sums of permutations with a given descent set. In fact, he showed that every Coxeter group has something that can be called a descent algebra. There is also a commutative, semisimple subalgebra of Solomon’s descent algebra generated by sums of permutations with the sam...

we present an improved version of a full nesterov-todd step infeasible interior-point method for linear complementarityproblem over symmetric cone (bull. iranian math. soc.,40(3), 541-564, (2014)). in the earlier version, each iteration consistedof one so-called feasibility step and a few -at most three -centering steps. here, each iteration consists of only a feasibilitystep. thus, the new alg...

For a Coxeter group (W,S), a permutation of the set S is called a Coxeter word and the group element represented by the product is called a Coxeter element. Moving the first letter to the end of the word is called a rotation and two Coxeter elements are rotation equivalent if their words can be transformed into each other through a sequence of rotations and legal commutations. We prove that Cox...

Complete presentations provide a natural solution to the word problem in monoids and groups. Here we give a simple way to construct complete presentations for the direct product of groups, when such presentations are available for the factors. Actually, the construction we are referring to is just the classical construction for direct products of groups, which has been known for a long time, bu...

In mathematics, a group is the set of symmetries of an object. Coxeter groups are a broad and natural class of groups that are related to reflectional symmetries. Each Coxeter group is determined by a diagram, called a labeled graph, that encodes algebraic information about the group. In general, two different labeled graphs can give rise to the same group. It is therefore natural to ask: are t...

We study combinatorial aspects of the representation theory of the 0-Hecke algebra Hn(0), a deformation of the group algebra of the symmetric group Sn. We study the action of Hn(0) on the polynomial ring in n variables. We show that the coinvariant algebra of this action naturally carries the regular representation of Hn(0), giving an analogue of the well-known result for the symmetric group by...