#### Filter Results:

- Full text PDF available (12)

#### Publication Year

2003

2014

- This year (0)
- Last 5 years (1)
- Last 10 years (9)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Samuel K. Hsiao
- Electr. J. Comb.
- 2009

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 ΣGn associated with G ≀ Sn, the wreath product of the symmetric group Sn with an arbitrary group G. Techniques of Bidigare and Brown are adapted to construct an… (More)

- Marcelo Aguiar, Samuel K. Hsiao
- Electr. J. Comb.
- 2005

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 halfintegers, or in… (More)

- Samuel K. Hsiao
- 2008

The colored quasisymmetric functions, like the classic quasisymmetric functions, are known to form a Hopf algebra with a natural peak subalgebra. We show how these algebras arise as the image of the algebra of colored posets. To effect this approach we introduce colored analogs of P -partitions and enriched P -partitions. We also frame our results in terms… (More)

Via duality of Hopf algebras, there is a direct association between peak quasisymmetric functions and enumeration of chains in Eulerian posets. We study this association explicitly, showing that the notion of cd-index, long studied in the context of convex polytopes and Eulerian posets, arises as the dual basis to a natural basis of peak quasisymmetric… (More)

- Samuel K. Hsiao
- 2007

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 important random walks are now realized this way: Stanley’s QS-distribution results from endomorphisms given by… (More)

- Louis J. Billera, Samuel K. Hsiao, J. Scott Provan
- Discrete & Computational Geometry
- 2008

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)

- Samuel K. Hsiao
- J. Comb. Theory, Ser. A
- 2006

We construct a family of posets, called signed Birkhoff posets, that may be viewed as signed analogs of distributive lattices. Our posets are generally not lattices, but they are shown to posses many combinatorial properties corresponding to well known properties of distributive lattices. They have the additional virtue of being face posets of regular cell… (More)

- John Cullinan, Samuel K. Hsiao, David Polett
- Social Choice and Welfare
- 2014

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 show that with the appropriate choice of coproduct, the type B quasisymmetric functions form a Hopf algebra, and the recently introduced type B peak functions form a Hopf subalgebra. In this note we show that the type B quasisymmetric functions form a Hopf algebra in a natural way, and that the type B peak functions of [7] are a Hopf subalgebra. A future… (More)

- Marcelo Aguiar, Carlos André, +23 authors Mike Zabrocki
- 2011

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)