249 citations · 413 across the 7 of their papers we have counts for
7 papers
A combinatorial formula for non-symmetric Macdonald polynomials
J. Haglund, M. Haiman, N. Loehr
We give a combinatorial formula for the non-symmetric Macdonald polynomials E_μ(x;q,t). The formula generalizes our previous combinatorial interpretation of the integral form symme…
A Combinatorial Formula for Macdonald Polynomials
J. Haglund, M. Haiman, N. Loehr
We prove a combinatorial formula for the Macdonald polynomial H_mu(x;q,t) which had been conjectured by the first author. Corollaries to our main theorem include the expansion of H…
A Combinatorial Formula for the Character of the Diagonal Coinvariants
J. Haglund, M. Haiman, N. Loehr +2
Let R_n be the ring of coinvariants for the diagonal action of the symmetric group S_n. It is known that the character of R_n as a doubly-graded S_n module can be expressed using t…
Multigraded Hilbert Schemes
Mark Haiman, Bernd Sturmfels
We introduce the multigraded Hilbert scheme, which parametrizes all homogeneous ideals with fixed Hilbert function in a polynomial ring that is graded by any abelian group. Our con…
Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
Mark Haiman
Earlier we showed that the Hilbert scheme of points in the plane can be identified with the Hilbert scheme of regular orbits on . Using this result, together with…
Hilbert schemes, polygraphs, and the Macdonald positivity conjecture
Mark Haiman
We study the isospectral Hilbert scheme X_n, defined as the reduced fiber product of C^2n with the Hilbert scheme H_n of points in the plane, over the symmetric power S^n C^2. We p…