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...
We prove that the translation plane and the shift plane defined by a planar partition function form an oval pair of projective planes in the sense that the planes share a line pe...
The relationship between the length of a word and the maximum length of its unbordered factors is investigated in this paper. Consider a finite word w of length n. We call a word...
A d-regular graph has largest or first (adjacency matrix) eigenvalue 1 = d. Consider for an even d 4, a random d-regular graph model formed from d/2 uniform, independent permutat...