#### Filter Results:

#### Publication Year

2007

2013

#### Publication Type

#### Co-author

#### Key Phrase

#### Publication Venue

Learn More

The aim of the paper is to calculate face numbers of simple generalized permutohedra, and study their f-, hand γ-vectors. These polytopes include permutohedra, associahedra, graph-associahedra, simple graphic zonotopes, nestohedra, and other interesting polytopes. We give several explicit formulas for h-vectors and γ-vectors involving descent statistics.… (More)

- Nan Li, Richard P Stanley, Alex Postnikov, Amos, Steven V Sam, Yan Zhang +3 others
- 2013

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)

- Hs@bullettinsnt E, B S, S, Sergiy Sidenko, Richard Dudley, Alex Postnikov +2 others
- 2008

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)

- Ira Gessel, Ji Li, Adam Jaffe, Susan Parker, Alex Postnikov, To Kailang +6 others
- 2007

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)

- ‹
- 1
- ›