Irene Müller
(ETH Zürich)
On corner cut polytopes
Abstract: Corner cut polytopes (or staircase polytopes) were first defined by S. Onn and B. Sturmfels. The vertices of these polytopes are in one-to-one correspondence to certain partitions of natural numbers, so called corner cuts. Due to this correspondence, advances in counting corner cuts were achieved.
We discuss some structural, nonetheless esthetic aspects of corner cut polytopes. In the two-dimensional case, we draw a connection between a natural linear order on the vertices and a classical partial order on partitions. Furthermore, we investigate the relationship between corner cuts and the face structure of the associated corner cut polytope.