CONVEX POLYTOPES AND ENUMERATION

This is an expository paper on connections between enumerative combina torics and convex polytopes. It aims to give an essentially self-conta ined overview of five specific instances when enumerative combinatoric s and convex polytopes arise jointly in problems whose initial formula tion lies in only one of these two subjects. These examples constitute only a sample of such instances occurring in the work of several auth ors. On the enumerative side, they involved ordered graphical sequence s, combinatorial statistics on the symmetric and hyperoctahedral group s, lattice paths, Baxter, Andre, and simsun permutations, q-Catalan an d q-Schroder numbers. From the subject of polytopes, the examples invo lve the Ehrhart polynomial, the permutohedron, the associahedron, poly topes arising as intersections of cubes and simplices with half-spaces , and the cd-index of a polytope. (C) 1997 Academic Press.