Vertex Cones of Order Polytopes
Elijah Valverde
Department of Mathematics
Faculty Supervisor: Matthias Beck
An order polytope is a natural polyhedral image of a given poset. It was defined in the 80s by Stanley and has since appeared in many applications. The vertex cone of a polytope $P$ at $v$ is the smallest affine cone with apex $v$ that contains $P$ . It makes an appearance, among other things, in Brion’s theorem, decomposing the integer- point transform of P into that of its vertex cones. We will study the combinatorics and arithmetic (i.e., integer-point transforms) of vertex cones of an order polytope.