# Meeting Details

Title: Permutohedral Arrangements, Simplicial Decompositions and a Geometrization of the Classical Worpitzky Identity Applied Algebra and Network Theory Seminar Nick Early, Penn State In forthcoming joint work with Adrian Ocneanu, we prove a symmetric group character formula conjectured several years ago by the latter as he was studying certain polyhedra emerging from hyperplane arrangements in simplices. We reveal the geometric content which lies behind the classical Worpitzky identity, which expands a cubical number $r^{n-1}$ in terms of the Eulerian numbers. Our proof suggests a new geometric interpretation of combinatorial results of Sagan-Shareshian-Wachs on Eulerian quasi-symmetric functions.