15 citations · 104 across the 38 of their papers we have counts for
11 papers · 1 filter
The Antipodes of -Quasi-Symmetric Functions and Non-Commutative Quasi-Symmetric Functions
Shaul Zemel
We prove the antipode formula for the -deformations of quasi-symmetric functions. We also define a fundamental basis for non-commutative quasi-symmetric functions, and establish…
Polynomial Expressions for Symmetric Group Characters on Cycles
Tom Moshaiov, Shaul Zemel
In \cite{[CZ]}, Cohen and Zemel showed that for a partition , the dimension of the irreducible representation of corresponding to the partition $(n-k,λ) \vdash n…
Generalized Higher Specht Polynomials and Homogeneous Representations of Symmetric Groups
Shaul Zemel
We consider actions, similar to those of Haglund, Rhoades, and Shimozono on ordered partitions, and their basis in terms of the higher Specht polynomials of Ariki, Terasoma, and Ya…
Compatibility of Higher Specht Polynomials and Decompositions of Representations
Shaul Zemel
%We show how to normalize the higher Specht polynomials of Ariki, Terasoma, and Yamada in a compatible way in order to define a stable version of these polynomials. We also decompo…
Generating Series of Key Polynomials and Bounded Ascending Sequences of Integers
Noah Cape, Shaul Zemel
The fact that Schubert polynomials are the weighted counting functions for reduced RC-graphs, also known as reduced pipe dreams, was established using their generating functions in…
Polynomial Expressions for the Dimensions of the Representations of Symmetric Groups and Restricted Standard Young Tableaux
Avichai Cohen, Shaul Zemel
Given a partition of a number , it is known that by adding a long line of length , the dimension of the associated representation of is an integer-valued polyno…
Polynomial Divided Difference Operators Satisfying the Braid Relations
Shaul Zemel
Many interesting families of polynomials are indexed by permutations or related objects, and are defined by applying divided difference operators, modified by polynomials, on some…
On Higher Partial Derivatives of Implicit Functions and their Combinatorics
Shaul Zemel
We consider a scalar-valued implicit function of many variables, and provide two closed formulae for all of its partial derivatives. One formula is based on products of partial der…
Moments of Partitions and Derivatives of Higher Order
Shaul Zemel
We Define moments of partitions of integers, and show that they appear in higher order derivatives of certain combinations of functions.
The Combinatorics of Higher Derivatives of Implicit Functions
Shaul Zemel
We prove a closed formula for the derivative, of any order, of a implicit function, in terms of some binomial building blocks, and explain the combinatorics behind the coefficients…
Generalized Riordan Groups and Operators on Polynomials
Shaul Zemel
We present an approach to generalized Riordan arrays which is based on operations in one large group of lower triangular matrices. This allows for direct proofs of many properties…