A very fundamental geometric problem on finite systems of spheres was independently phrased by Kneser (1955) and Poulsen (1954). According to their well-known conjecture if a fi...
We prove that coloring a 3-uniform 2-colorable hypergraph with c colors is NP-hard for any constant c. The best known algorithm [20] colors such a graph using O(n1/5 ) colors. Our...
We prove a combinatorial formula conjectured by Loehr and Warrington for the coefficient of the sign character in (pn). Here denotes the Bergeron-Garsia nabla operator, and pn is a...
Haglund and Loehr previously conjectured two equivalent combinatorial formulas for the Hilbert series of the Garsia-Haiman diagonal harmonics modules. These formulas involve weigh...