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Astract We study here the ring QS n of Quasi-Symmetric Functions in the variables x 1 , x 2 ,. .. , x n. F. Bergeron and C. Reutenauer [4] formulated a number of conjectures about this ring, in particular they conjectured that it is free over the ring Λ n of symmetric functions in x 1 , x 2 ,. .. , x n. We present here an algorithm that recursively(More)
The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there(More)
In this paper we announce a qualitative description of an important class of closed n-dimensional submanifolds of the m-dimensional sphere, namely, those which locally minimize the n-area in the same way that geodesics minimize the arc length and are themselves locally n-spheres of constant radius r; those r that may appear are called admissible. It is(More)