4 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…
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…
Lusztig -weight multiplicities and Kirillov-Reshetikhin crystals
Hyeonjae Choi, Donghyun Kim, Seung Jin Lee
Lusztig -weight multiplicities extend the Kostka-Foulkes polynomials to a broader range of Lie types. In this work, we investigate these multiplicities through the framework of…
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 conjec…