2 problems

Let $R_n^{(3,0)}$ denote the $(3,0)$-bosonic coinvariant ring. Haiman's conjecture. Its dimension is … This conjecture was made by Haiman in 1994 and remains open in general.

Let $R_n^{(1,2)}$ be the $(1,2)$ bosonic-fermionic coinvariant ring, and let $B_n^{(1,2)}$ be the monomial set constructed by interpolating between the Kim–Rhoades basis and the su…