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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.

- Alon Regev, Amitai Regev, Doron Zeilberger
- 2015

We use the algebra of difference operators to study sums of squares (and other powers) of the characters of the symmetric group, χ λ (µ), when the sum is restricted over shapes, λ, with a fixed number of rows, and for hook shapes, and µ has 'mostly' ones. We prove that such sums are always P-recursive, i.e., satisfy a linear difference equation with… (More)

- Amitai Regev, Nathaniel Shar, Doron Zeilberger, Dominique Gouyo-Beauchamp, Kyle Petersen, Dennis Stanton
- 2015

Recall that one of the almost infinitely many definitions of the ubiquitous Catalan Numbers, C n , is as the number of elements of the set of 2n-letter words, w 1. .. w 2n in the alphabet {−1, 1} that add up to zero, and all whose partial sums are non-negative. Let's call this set C n. In the 1924 Toronto ICM, Jacques Touchard [T] announced (and proved) the… (More)

In a recent article, we noted (and proved) that the sum of the squares of the characters of the symmetric group, χ λ (µ), over all shapes λ with two rows and n cells and µ = 31 n−3 , equals, surprisingly, to 1/2 of that sum-of-squares taken over all hook shapes with n + 2 cells and with µ = 321 n−3. In the present note, we show that this is only the tip of… (More)