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Every character on a graded connected Hopf algebra decomposes uniquely as a product of an even character and an odd character [2]. We obtain explicit formulas for the even and odd parts of the universal character on the Hopf algebra of quasi-symmetric functions. They can be described in terms of Legendre's beta function evaluated at half-integers, or in(More)
There is a well-known combinatorial definition, based on ordered set partitions, of the semigroup of faces of the braid arrangement. We generalize this definition to obtain a semigroup Σ G n associated with G ≀ S n , the wreath product of the symmetric group S n with an arbitrary group G. Techniques of Bidigare and Brown are adapted to construct an(More)
We construct CW spheres from the lattices that arise as the closed sets of a convex closure, the meet-distributive lattices. These spheres are nearly polytopal, in the sense that their barycentric subdivisions are simplicial polytopes. The complete information on the numbers of faces and chains of faces in these spheres can be obtained from the defining(More)
Conditions are provided under which an endomorphism on quasisymmetric functions gives rise to a left random walk on the descent algebra which is also a lumping of a left random walk on permutations. Spectral results are also obtained. Several well-studied random walks are now realized this way: Stanley's QS-distribution results from endomor-phisms given by(More)
The application of the theory of partially ordered sets to voting systems is an important development in the mathematical theory of elections. Many of the results in this area are on the comparative properties between traditional elections with linearly ordered ballots and those with partially ordered ballots. In this paper we present a scoring procedure,(More)
We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be(More)
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