Amitai Regev

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Let An ⊆ Sn 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 Sn, has received far reaching refinements and generalizations, by Foata [5], Carlitz [3, 4], FoataSchützenberger [6], Garsia-Gessel [7] and followers. Our main goal is to find analogous(More)
We introduce and study a family {FSμ} of symmetric functions which we call the Frobenius–Schur functions. These are inhomogeneous functions indexed by partitions and such that FSμ differs from the conventional Schur function sμ in lower terms only. Our interest in these new functions comes from the fact that they provide an explicit expression for dim ν/μ(More)
Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition μ, we deduce several skew diagrams which are related to μ. 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 = w1 · · ·wn, 1 ≤ wi ≤ k, for which there are 1 ≤ i1 < · · · < i` ≤ n and wi1 > · · · > wi` , is given, by the Schensted-Knuth correspondence, in terms of standard and semi-standard Young tableaux. When n → ∞, the asymptotics of the number of such words is calculated. Work partially supported by N.S.F. Grant No. DMS-94-01197.
Natural q analogues of classical statistics on the symmetric groups Sn 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)
Let V ⊗n be the n–fold tensor product of a vector space V. Following I. Schur we consider the action of the symmetric group Sn on V ⊗n by permuting coordinates. In the ‘super’ (Z2 graded) case V = V0 ⊕ V1, a ± sign is added [BR]. These actions give rise to the corresponding Schur algebras S(Sn, V ). Here S(Sn, V ) is compared with S(An, V ), the Schur(More)