15 citations · 24 across the 6 of their papers we have counts for
7 papers
Deformation of Cayley's hyperdeterminants
Tommy Wuxing Cai, Naihuan Jing
We introduce a deformation of Cayley's second hyperdeterminant for even-dimensional hypermatrices. As an application, we formulate a generalization of the Jacobi-Trudi formula for…
Average length of the longest -alternating subsequence
Tommy Wuxing Cai
We prove a conjecture of Drew Armstrong on the average maximal length of -alternating subsequence of permutations. The case is a well-known result of Richard Stanley.
Macdonald symmetric functions of rectangular shapes
Tommy Wuxing Cai
Using vertex operator we study Macdonald symmetric functions of rectangular shapes and their connection with the q-Dyson Laurent polynomial. We find a vertex operator realization o…
A generalization of Newton's identity and Macdonald functions
Wuxing Cai, Naihuan Jing
A generalization of Newton's identity on symmetric functions is given. Using the generalized Newton identity we give a unified method to show the existence of Hall-Littlewood, Jack…
Generalized McKay quivers of rank three
Xiaoli Hu, Naihuan Jing, Wuxing Cai
For each finite subgroup G of SL(n, C), we introduce the generalized Cartan matrix C_{G} in view of McKay correspondence from the fusion rule of its natural representation. Using g…
Applications of Laplace-Beltrami operator for Jack polynomials
Wuxing Cai, Naihuan Jing
We use a new method to study the Laplace-Beltrami type operator on the Fock space of symmetric functions, and as an example of our explicit computation we show that the Jack symmet…