A Multi-Set Identity for Partitions (2009)
Regev, Amitai, Zeilberger, Doron
We prove that the multiset {(RightArmLength,LeftArmLength)} ranging over all cells of all Ferrers diagrams with n cells equals the multiset {(RightArmLength,LegLength)} ranging over all cells of all...
E-Mail: Regev@math.psu.edu (2007)
. The number of words w = w 1 w n ,1# w i # k, for which there are 1 # i 1 < <i # # n and w i 1 > >w i # , is given, by the Schensted-Knuth correspondence, in terms of standard and...
Amitai Regev, Doron Zeilberger
The notion of hook number was originally defined for the cells of the Young diagram D(a): = f(i; j) j 1 j k; 1 i a k\Gammaj+1 g of a partition a = (a 1; : : : ; a k). The hook number, h(x), of a cell...
Random Young tableaux and combinatorial identities, http:// arXiv.org/abs/math.CO/0106074 (2007)
Grigori Olshanski, Amitai Regev
Abstract. We derive new combinatorial identities which may be viewed as multivariate analogs of summation formulas for hypergeometric series. As in the previous paper [Re], we start with probability...
Expected lengths and distribution functions for Young diagrams in the hook (2005)
We consider $\beta$--Plancherel measures \cite{Ba.Ra.} on subsets of partitions -- and their asymptotics. These subsets are the Young diagrams contained in a $(k,\ell)$--hook, and we calculate the...
A Foata bijection for the alternating group and for q analogues (2005)
The Foata bijection $\Phi : S_n \to S_n$ is extended to the bijections $\Psi : A_{n+1} \to A_{n+1}$ and $\Psi_q : S_{n+q-1} \to S_{n+q-1}$, where S_m, A_m are the symmetric and the alternating...
Statistics on Wreath Products and Generalized Binomial-Stirling Numbers (2004)
Regev, Amitai, Roichman, Yuval
Various statistics on wreath products are defined via canonical words, "colored" right to left minima and "colored" descents. It is shown that refined counts with respect to these statistics have...
q Statistics on $S_n$ and Pattern Avoidance (2003)
Regev, Amitai, Roichman, Yuval
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...
Permutation Statistics on the Alternating Group (2003)
Regev, Amitai, Roichman, Yuval
Let $A_n\subseteq S_n$ denote the alternating and the symmetric groups on $1,...,n$. MacMahaon's theorem, about the equi-distribution of the length and the major indices in $S_n$, has received far...
Frobenius-Schur functions (2001)
Olshanski, Grigori, Regev, Amitai, Vershik, Anatoly
The present paper is a detailed version of math/0003031. We introduce and study a new basis in the algebra of symmetric functions. The elements of this basis are called the Frobenius-Schur functions...
Double Centralizing Theorems for the Alternating Groups (2001)
Let $V^{\otimes n}$ be the $n$-fold tensor product of a vector space $V.$ Following I. Schur we consider the action of the symmetric group $S_n$ on $V^{\otimes n}$ by permuting coordinates. In the...
Random Young Tableaux and Combinatorial Identities (2001)
Olshanski, Grigori, Regev, Amitai
We derive new combinatorial identities which may be viewed as multivariate analogs of summation formulas for hypergeometric series. As in the previous paper [Re], we start with probability...
Shuffle Invariance of the Super-RSK Algorithm (2001)
As in the $(k,l)$-RSK (Robinson-Schensted-Knuth) of [1], other super-RSK algorithms can be applied to sequences of variables from the set $\{t_1,...,t_k,u_1,...,u_l\}$, where $t_1
Frobenius-Schur functions: summary of results (2000)
Olshanski, Grigori, Regev, Amitai, Vershik, Anatoly
We introduce and study a family of inhomogeneous symmetric functions which we call the Frobenius-Schur functions. These functions are indexed by partitions and differ from the conventional Schur...
Frobenius-Schur Functions (1999)
Grigori Olshanski, Amitai Regev, Anatoly Vershik
We introduce and study a new basis in the algebra of symmetric functions.
Asymptotics Of The Number Of (1998)
. The number of words w = w 1 \Delta \Delta \Delta w n , 1 w i k, for which there are 1 i 1 ! \Delta \Delta \Delta ! i ` n and w i 1 ? \Delta \Delta \Delta ? w i ` , is given, by the Schensted-Knuth...
Asymptotics Of The Number Of k-Words With An l-Descent (1998)
. The number of words w = w 1 w n,1#w i #k, for which there are 1 # i 1 < <i # #nand w i 1 > >w i # , is given, by the Schensted-Knuth correspondence, in terms of standard and...
Asymptotics of the Number of k-Words with an l-Descent (1998)
. The number of words w = w 1 \Delta \Delta \Delta wn , 1 w i k, for which there are 1 i 1 ! \Delta \Delta \Delta ! i ` n and w i 1 ? \Delta \Delta \Delta ? w i ` , is given, by the Schensted-Knuth...
Asymptotics of Young diagrams and hook numbers (1997)
Amitai Regev, Anatoly Vershik, Givat Ram
Abstract: 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...
Asymptotics of Young diagrams and hook numbers (1997)
Amitai Regev, Anatoly Vershik, Givat Ram
Abstract: 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...
Asymptotics of Young Diagrams and Hook Numbers (1997)
Amitai Regev, Anatoly Vershik, Givat Ram
: 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...
Proof Of The Alternating Sign Matrix Conjecture (1995)
Doron Zeilberger, Gert Almkvist, Noga Alon, George Andrews, Dror Bar-natan, Francois Bergeron, ...
: The number of n n matrices whose entries are either -1, 0, or 1, whose row- and column- sums are all 1, and such that in every row and every column the non-zero entries alternate in sign, is proved...