Convex Polytopes and Enumeration

✍ Scribed by Rodica Simion

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 311 KB
• Volume: 18
• Category: Article
• ISSN: 0196-8858
• DOI: 10.1006/aama.1996.0505

✦ Synopsis

This is an expository paper on connections between enumerative combinatorics and convex polytopes. It aims to give an essentially self-contained overview of five specific instances when enumerative combinatorics and convex polytopes arise jointly in problems whose initial formulation lies in only one of these two subjects. These examples constitute only a sample of such instances occurring in the work of several authors. On the enumerative side, they involved ordered graphical sequences, combinatorial statistics on the symmetric and hyperoctahedral groups, lattice paths, Baxter, Andre, and simsun permutations, q-Catalan and q-Schroder ´numbers.

From the subject of polytopes, the examples involve the Ehrhart polynomial, the permutohedron, the associahedron, polytopes arising as intersections of cubes and simplices with half-spaces, and the cd-index of a polytope.