Samuel K. Hsiao - Research

My research is in the areas of combinatorial Hopf algebras, enumerative combinatorics, and discrete geometry. I work with quasisymmetric functions, posets, simplicial complexes, convex polytopes, flag vectors, peaks, descents, random walks, and more.

• A semigroup approach to wreath-product extensions of Solomon's descent algebras, arXiv:0710.2081.
• Random walks on quasisymmetric functions, with Patricia Hersh, submitted, arXiv:0709.1477.
• Colored posets and colored quasisymmetric functions, with T. Kyle Petersen, Annals of Combinatorics (to appear), math.CO/0610984.
• Enumeration in convex geometries and associated polytopal subdivisions of spheres, with Louis J. Billera and J. Scott Provan Discrete and Computational Geometry 39 (2008), no. 1, 123-137math.CO/0505576.
• • A signed analog of the Birkhoff transform, Journal of Combinatorial Theory Series A 113 (2006), no. 2, 251-272 Download preprint.
  • A signed analog of the Birkhoff transform, extended abstract, Proceedings of the 16th Annual Conference on Formal Power Series and Algebraic Combinatorics (2004). Download preprint.
• Canonical characters on quasi-symmetric functions and bivariate Catalan numbers, with Marcelo Aguiar, Electronic Journal of Combinatorics, Stanley Festschrift, Vol 11(2) (2005), R15. To journal.
• Peak quasisymmetric functions and Eulerian enumeration, with L. Billera and S. van Willigenburg, Advances in Mathematics 176 (2003), no. 2, 248-276. Download preprint (ps).

• The Hopf algebras of type B quasisymmetric functions and peak functions, with T. Kyle Petersen, October 2006. math.CO/0610976.
• Structure of the peak Hopf algebra of quasisymmetric functions, January 2003. Download pdf.