Related papers: Comultiplication rules for the double Schur functi…
Using symmetric function theory, we study the cycle structure and increasing subsequence structure of permutations after various shuffling methods, emphasizing the role of Cauchy type identities and the Robinson-Schensted-Knuth…
The Bernstein operators allow to build recursively the Schur functions. We present a recursion formula for k-Schur functions at t=1 based on combinatorial operators that generalize the Bernstein operators. The recursion leads immediately to…
In this paper, we introduce a pair of multiplication-like operations, $L_0$ and $L_1$, which derive $k$-regular functions from $(k+1)$-regular functions. The investigation of the inverse problem naturally leads to a deeper study of the…
Recently a new basis for the Hopf algebra of quasisymmetric functions $QSym$, called quasisymmetric Schur functions, has been introduced by Haglund, Luoto, Mason, van Willigenburg. In this paper we extend the definition of quasisymmetric…
This paper deals with decreasing operators on back stable Schubert polynomials. We study two operators $\xi$ and $\nabla$ of degree $-1$, which satisfy the Leibniz rule. Furthermore, we show that all other such operators are linear…
A Schur multiplier is a linear map on matrices which acts on its entries by multiplication with some function, called the symbol. We consider idempotent Schur multipliers, whose symbols are indicator functions of smooth Euclidean domains.…
We introduce the notion of a two-scale branching function associated with an arbitrary metric space, which encodes the lower and upper box dimensions as well as the Assouad spectrum. If the metric space is quasi-doubling, this function is…
We obtain the Schur positivity of spider graphs of the forms $S(a,2,1)$ and $S(a,4,1)$, which are considered to have the simpliest structures for which the Schur positivity was unknown. The proof outline has four steps. First, we find…
We introduce the quantum multi-Schur functions, quantum factorial Schur functions and quantum Macdonald polynomials. We prove that for restricted vexillary permutations the quantum double Schubert polynomial coincides with some quantum…
The dual immaculate and Young quasisymmetric Schur bases of quasisymmetric functions possess analogues in the peak algebra: respectively, the quasisymmetric Schur $Q$-functions and the peak Young quasisymmetric Schur functions. We show…
An element [\Phi] of the Grassmannian of n-dimensional subspaces of the Hardy space H^2, extended over the field C(x_1,..., x_n), may be associated to any polynomial basis {\phi} for C(x). The Pl\"ucker coordinates…
We consider an operator of Bernstein for symmetric functions, and give an explicit formula for its action on an arbitrary Schur function. This formula is given in a remarkably simple form when written in terms of some notation based on the…
The Kronecker product of two Schur functions $s_{\mu}$ and $s_{\nu}$, denoted by $s_{\mu}*s_{\nu}$, is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the…
In this paper, using the theory of category, we generalize known properties of symmetric polynomials and functions and characterize the multi-indicial symmetric functions. Examples have been given on Schur functions.
We provide a generalization of the Littlewood identity, both sides of which are related to alternating sign matrices. The classical Littlewood identity establishes a nice product formula for the sum of all Schur polynomials. Compared to the…
Using cocommutativity of the Hopf algebra of symmetric functions, certain skew Schur functions are proved to be equal. Some of these skew Schur function identities are new.
Let $\Lambda$ be the space of symmetric functions and $V_k$ be the subspace spanned by the modified Schur functions $\{S_\lambda[X/(1-t)]\}_{\lambda_1\leq k}$. We introduce a new family of symmetric polynomials,…
Multi-Schur functions are symmetric functions that generalize the supersymmetric Schur functions, the flagged Schur functions, and the refined dual Grothendieck functions, which have been intensively studied by Lascoux. In this paper, we…
Closed forms for $f_{\lambda,i} (q) := \sum_{\tau \in SYT(\lambda) : des(\tau) = i} q^{maj(\tau)}$, the distribution of the major index over standard Young tableaux of given shapes and specified number of descents, are established for a…
Using Schur positivity and the principal specialization of Schur functions, we provide a proof of a recent conjecture of Liu and Wang on the $q$-log-convexity of the Narayana polynomials, and a proof of the second conjecture that the…