Let G1 and G2 be groups, G1 generated by a set A, and G2 generated by a set B. Let r = abcd, where a, c âˆˆ G1, and b, d âˆˆ G2. Let G = G1 âˆ— G2/ã€ˆã€ˆrã€‰ã€‰. We would like to classify the cases when theâ€¦ (More)

Modification of fatty acid composition of Hep-G2 cells was achieved by 7-9 days of supplementation of culture medium with palmitic, oleic or linoleic acid. Cholesterol release into serum-free cultureâ€¦ (More)

A classical result of MacMahon shows that the length function and the major index are equidistributed over the symmetric group. A long standing open problem is to extend the notion of major index andâ€¦ (More)

Let C(T ) be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either Bn or Dn. Let CY (T ) be a natural quotient of C(T ), and if C(T ) is simply-lacedâ€¦ (More)

We present recursions for the number of excedances in Coxeter groups of type A and B, as well as in the colored permutation groups Zr â‰€ Sn. The proofs use only computations of excedances.

We study certain quotients of generalized Artin groups which have a natural map onto D-type Artin groups, where the generalized Artin group A(T ) is defined by a signed graph T . Then we find aâ€¦ (More)

We define the excedence set and the excedance word on Gr,n, generalizing a work of Ehrenborg and Steingrimsson and use the inclusion-exclusion principle to calculate the number of coloredâ€¦ (More)

It is shown that, under mild conditions, a complex reflection group G(r, p, n) may be decomposed into a set-wise direct product of cyclic subgroups. This property is then used to extend the notion ofâ€¦ (More)