Enumerating wreath products via Garsia–Gessel bijections

Enumerating wreath products via Garsia-Gessel bijections

Abstract. We generalize two bijections due to Garsia and Gessel to compute the generating functions of the two vector statistics (desG,maj, lG, col) and (desG, idesG,maj, imaj, col, icol) over the wreath product of a symmetric group by a cyclic group. Here desG, lG, maj, col, idesG, imajG, and icol denote the number of descents, length, major index, color weight, inverse descents, inverse major...

The Wreath Products

Rooted Wreath Products

We introduce “rooted valuation products” and use them to construct universal Abelian lattice-ordered groups (with prescribed set of components) [CHH] from the more classical theory of [Ha]. The Wreath product construction of [H] and [HMc] generalised the Abelian (lattice-ordered) group ideas to a permutation group setting to respectively give universals for transitive (`-) permutation groups wi...

Coupled Cells: Wreath Products and Direct Products

In this note we discuss the structure of systems of coupled cells (which we view as systems of ordinary differential equations) where symmetries of the system are obtained through the group G of global permutations of the cells and the group L of local internal symmetries of the dynamics in each cell. We show that even when the cells are assumed to be identical with identical coupling, the way ...

Eigenvalues of Random Wreath Products

Steven N. Evans Department of Statistics #3860, University of California at Berkeley 367 Evans Hall, Berkeley, CA 94720-3860, U.S.A [email protected] Abstract Consider a uniformly chosen element Xn of the n-fold wreath product Γn = G o G o · · · o G, where G is a finite permutation group acting transitively on some set of size s. The eigenvalues of Xn in the natural sn-dimensional permuta...