We define an excedance number for the multi-colored permutation group i.e. the wreath product Zr1 × · · ·×Zrk ≀Sn and calculate its multi-distribution with some natural parameters. We also compute the multi-distribution of the parameters exc(π) and fix(π) over the sets of involutions in the multi-colored permutation group. Using this, we count the number of involutions in this group having a fi...

Let X be a definable sub-set of some o-minimal structure. We study the spectrum of X , in relation with the definability of types.