Related papers: A Murnaghan-Nakayama Rule For Noncommutative Schur…
We establish new Murnaghan--Nakayama rules for symplectic, orthogonal and orthosymplectic Schur functions. The classical Murnaghan--Nakayama rule expresses the product of a power sum symmetric function with a Schur function as a linear…
We prove the Murgnaghan--Nakayama rule for $k$-Schur functions of Lapointe and Morse, that is, we give an explicit formula for the expansion of the product of a power sum symmetric function and a $k$-Schur function in terms of $k$-Schur…
We continue our development of a new basis for the algebra of non-commutative symmetric functions. This basis is analogous to the Schur basis for the algebra of symmetric functions, and it shares many of its wonderful properties. For…
The Murnaghan-Nakayama rule expresses the product of a Schur function with a Newton power sum in the basis of Schur functions. We establish a version of the Murnaghan-Nakayama rule for Schubert polynomials and a version for the quantum…
We give a combinatorial proof of a natural generalization of the Murnaghan-Nakayama rule to loop Schur functions. We also define shifted loop Schur functions and prove that they satisfy a similar relation.
Lam and Pylyavskyy introduced loop symmetric functions as a generalization of symmetric functions. They defined loop Schur functions as generating functions over semistandard tableaux with respect to a `colored weight,' and they proved a…
The plethystic Murnaghan-Nakayama rule describes how to decompose the product of a Schur function and a plethysm of the form $p_r\circ h_m$ as a sum of Schur functions. We provide a short, entirely combinatorial proof of this rule using the…
The $K$-$k$-Schur functions and $k$-Schur functions appeared in the study of $K$-theoretic and affine Schubert Calculus as polynomial representatives of Schubert classes. In this paper, we introduce a new family of symmetric functions…
We generalize several classical results about Schur functions to the family of cylindric Schur functions. First, we give a combinatorial proof of a Murnaghan--Nakayama formula for expanding cylindric Schur functions in the power-sum basis.…
This article gives a combinatorial proof of a plethystic generalization of the Murnaghan--Nakayama rule. The main result expresses the product of a Schur function with the plethysm $p_r \circ h_n$ as an integral linear combination of Schur…
In 2004 Rosas and Sagan asked whether there was a way to define a basis in the algebra of symmetric functions in noncommuting variables, NCSym, having properties analogous to the classical Schur functions. This was because they had…
As a spin analog of the plethystic Murnaghan-Nakayama rule for Schur functions, the plethystic Murnaghan-Nakayama rule for Schur $Q$-functions is established with the help of the vertex operator realization. This generalizes both the…
The theory of noncommutative Schur functions can be used to obtain positive combinatorial formulae for the Schur expansion of various classes of symmetric functions, as shown by Fomin and Greene. We develop a theory of noncommutative super…
Given an identity relating families of Schur and power sum symmetric functions, this may be thought of as encoding representation-theoretic properties according to how the $p$-to-$s$ transition matrices provide the irreducible character…
The $(P, w)$-partition generating function $K_{(P,w)}(x)$ is a quasisymmetric function obtained from a labeled poset. Recently, Liu and Weselcouch gave a formula for the coefficients of $K_{(P,w)}(x)$ when expanded in the quasisymmetric…
Based on the vertex operator realization of the Schur functions, a determinant-type plethystic Murnaghan--Nakayama rule is obtained and utilized to derive a general formula of the expansion coefficients of $s_{\nu}$ in the plethysm product…
In this paper, we extend recent results of Assaf and McNamara on skew Pieri rule and skew Murnaghan-Nakayama rule to a more general identity, which gives an elegant expansion of the product of a skew Schur function with a quantum power sum…
The Murnaghan--Nakayama rule is a combinatorial rule for the character values of symmetric groups. We give a new combinatorial proof by explicitly finding the trace of the representing matrices in the standard basis of Specht modules. This…
FPSAC 2013 Extended Abstract. We introduce a new basis of the non-commutative symmetric functions whose elements have Schur functions as their commutative images. Dually, we build a basis of the quasi-symmetric functions which expand…
We consider the Grothendieck polynomials appearing in the K-theory of Grassmannians, which are analogs of Schur polynomials. This paper aims to establish a version of the Murnaghan-Nakayama rule for Grothendieck polynomials of the…