The Permutahedral Variety, Mixed Eulerian Numbers, and Principal Specializations of Schubert Polynomials
The Permutahedral Variety, Mixed Eulerian Numbers, and Principal Specializations of Schubert Polynomials
Abstract We compute the expansion of the cohomology class of the permutahedral variety in the basis of Schubert classes. The resulting structure constants $a_w$ are expressed as a sum of normalized mixed Eulerian numbers indexed naturally by reduced words of $w$. The description implies that the $a_w$ are positive for …