Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition , we deduce several skew diagrams which are related to. To each such skew diagram there corresponds the product of its hook numbers. By asymptotic methods we obtain some unexpected arithmetic properties between… (More)
The number of words w = w 1 w n , 1 w i k, standard and semi-standard Young tableaux. When n ! 1, the asymptotics of the number of such words is calculated.
Natural q analogues of classical statistics on the symmetric groups S n are introduced; parameters like: the q-length, the q-inversion number , the q-descent number and the q-major index. MacMahon's theorem about the equi-distribution of the inversion number and the reverse major index is generalized to all positive integers q. It is also shown that the… (More)
We consider a certain decomposition of the matrix algebra M n (F), where F is a field.