The centers of gravity of the associahedron and of the permutahedron are the same.
The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles
The goal of this paper is to analyse the asymptotic behaviour of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens measure. We combine tools from combinatorics and complex analysis (e.g. singularity analysis of generating functions) to prove that under some analytic conditions (on relevant generating functions) the cycle process converges to a vector of independent Poisson variables...
The size of Fulton's essential set.
Trees in commtative nil-semigroups of index two