The purpose of this paper is to count permutations in S , with a given cycle structure and a given descent set. Our main result (Theorem 2.1) asserts that the number of these permutations can beâ€¦ (More)

Trees are a very basic object in computer science. They intervene in nearly a;ly domain, and they are studied for their own, or used to represent conveniently a given situation. There are at leastâ€¦ (More)

A descent class, in the symmetric group S,, is the collection of permutations with a given descent set. It was shown by L. Solomon (J. Algebra 41 (1976), 255-264) that the product (in the groupâ€¦ (More)

It is a well-known consequence of the elementary theory of vector spaces that if A and B are n-by-n matrices over a field (or even a skew field) such that AB = 1, then BA = 1. This result remainsâ€¦ (More)

Efforts to extract a Greenland ice core with a complete record of the Eemian interglacial (130,000 to 115,000 years ago) have until now been unsuccessful. The response of the Greenland ice sheet toâ€¦ (More)

We introduce a natural Hopf algebra structure on the space of noncommuta-tive symmetric functions which was recently studied as a vector space by Rosas and Sagan [12]. The bases for this algebra areâ€¦ (More)