5 papers · 1 filter
A skew Murnaghan--Nakayama rule for Hopf dual pairs
Naihuan Jing, Ning Liu
We develop a uniform skew Murnaghan--Nakayama theory for graded Hopf dual pairs equipped with a nondegenerate Hopf pairing. Using the completed Cauchy element, its grouplike factor…
On a Pieri-like rule for the Petrie symmetric functions
Emma Yu Jin, Naihuan Jing, Ning Liu
A -ribbon tiling is a decomposition of a connected skew diagram into disjoint ribbons of size . In this paper, we establish a connection between a subset of -ribbon tiling…
A spin analog of the plethystic Murnaghan-Nakayama rule
Yue Cao, Naihuan Jing, Ning Liu
As a spin analog of the plethystic Murnaghan-Nakayama rule for Schur functions, the plethystic Murnaghan-Nakayama rule for Schur -functions is established with the help of the v…
Irreducible characters and bitrace for the -rook monoid
Naihuan Jing, Yu Wu, Ning Liu
This paper studies irreducible characters of the -rook monoid algebra using the vertex algebraic method. Based on the Frobenius formula for , a new iterative ch…
A multiparametric Murnaghan-Nakayama rule for Macdonald polynomials
Naihuan Jing, Ning Liu
We introduce a new family of operators as multi-parameter deformation of the one-row Macdonald polynomials. The matrix coefficients of these operators acting on the space of symmet…