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Let A n ⊆ S n denote the alternating and the symmetric groups on 1,. .. , n. MacMahaon's theorem [11], about the equi-distribution of the length and the major indices in S n , has received far reaching refinements and generalizations, by Foata [5], Carlitz [3, 4], Foata-Schützenberger [6], Garsia-Gessel [7] and followers. Our main goal is to find analogous… (More)

We introduce and study a new basis in the algebra of symmetric functions. The elements of this basis are called the Frobenius{Schur functions (F S-functions, for short). Our main motivation for studying the F S-functions is the fact that they enter a formula expressing the combinatorial dimension of a skew Young diagram in terms of the Frobenius… (More)

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)

- Amitai Regev
- 1998

The number of words w = w 1 · · · w n , 1 ≤ w i ≤ k,

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)