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We studies two examples of polytope slices, hypersimplices as slices of hypercubes and edge polytopes. For hypersimplices, the main result is a proof of a conjecture by R. Stanley which gives an interpretation of the Ehrhart h*-vector in terms of descents and excedances. Our proof is geometric using a careful book-keeping of a shelling of a unimodular(More)
In the first part of this work, we study a long standing open problem on the mixing time of Kac's random walk on SO(n, R) by random rotations. We obtain an upper bound mix = O (n 2. 5 log n) for the weak convergence which is close to the trivial lower bound Q (n 2). This improves the upper bound O (n 4 log n) by Diaconis and Saloff-Coste 1131. The proof is(More)
The way is long with obstacles, I'm questing for the truth to and fro. iv Acknowledgments I would like to thank my advisor, Professor Ira Gessel, for his constant help and support, without which this work would never have existed. In this thesis, we enumerate different types of graphs in light of the combinatorial theory of species initiated by Joyal [13].(More)
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