6 papers
Shuffle theorem for torus link homology
Donghyun Kim, Jaeseong Oh
We prove that the symmetric function , arising from the elliptic Hall algebra, equals the generating function for -tuples of cyclic -parking…
Hadamard Products of dual Jacobi-Trudi matrices
Robert Angarone, Jang Soo Kim, Jaeseong Oh +1
We study positivity properties of Hadamard products of Jacobi-Trudi matrices. Maló proved that the Hadamard (entrywise) product of two totally positive upper-triangular Toeplitz m…
Total positivity of Hadamard product of dual Jacobi--Trudi matrices
Jang Soo Kim, Jaeseong Oh
In 1992, Wagner proved that the Hadamard product of two totally positive lower triangular Toeplitz matrices is totally positive. In this work, we strengthen this result by establis…
-chromatic symmetric functions
Jim Haglund, Jaeseong Oh, Meesue Yoo
In this paper, we introduce the \emph{-chromatic symmetric functions} , extending Shareshian and Wachs' chromatic symmetric functions with an additional real…
Refinement of Hikita's -positivity theorem via Abreu--Nigro's -functions and restricted modular law
JiSun Huh, Byung-Hak Hwang, Donghyun Kim +2
We study the symmetric functions \( g_{\mm,k}(x;q) \), introduced by Abreu and Nigro for a Hessenberg function \( \mm \) and a positive integer \( k \), which refine the chromatic…
Extending the science fiction and the Loehr--Warrington formula
Donghyun Kim, Jaeseong Oh
We introduce the Macdonald piece polynomial , which is a vast generalization of the Macdonald intersection polynomial in the science fiction conj…