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math.CO2007★ 1 cited
Random walks on quasisymmetric functions
Patricia Hersh, Samuel K. Hsiao
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 wal…
math.CO2007
Peak Quasisymmetric Functions and Eulerian Enumeration
Louis J. Billera, Samuel K. Hsiao, Stephanie van Willigenburg
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…
math.CO2005
Enumeration in convex geometries and associated polytopal subdivisions of spheres
Louis J. Billera, Samuel K. Hsiao, J. Scott Provan
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 t…