Let R be a root system with fixed basis ~' and let W be its Weyl group. For every element w ~ W, there exists a natural correspondence between reduced decompositions of w and some linear orders of the set of inversions of w. We study combinatorial properties of these orders. Furthermore, in the case of a symmetric group, for any permutation w we construct a linear action of the symmetric group ...

We generalize the results of Ksavrelof and Zeng about the multidistribution of the excedance number of Sn with some natural parameters to the colored permutation group and to the Coxeter group of type D. We define two different orders on these groups which induce two different excedance numbers. Surprisingly, in the case of the colored permutation group, we get the same generalized formulas for...

Dynamic pricing mechanisms occur on the Internet when buyers and sellers negotiate the final transaction price for the exchange of goods or services. These mechanisms are used in online auctions (e.g., eBay.com, uBid.com) and name-your-own-price (Priceline.com) formats, for example. The current research studies the dynamics of one instance of dynamic pricing -group-buying discounts -used by Mob...

We show that if H is an effectively completely decomposable computable torsion-free abelian group, then there is a computable copy G of H such that G has computable orders but not orders of every (Turing) degree.

Suppose that  is a finite group. Then the set of all prime divisors of  is denoted by  and the set of element orders of  is denoted by . Suppose that . Then the number of elements of order  in  is denoted by  and the sizes of the set of elements with the same order is denoted by ; that is, . In this paper, we prove that if  is a group such that , where , then . Here  denotes the family of Suzuk...