A constant term identity featuring the ubiquitous (and mysterious) Andrews-Mills-Robbins-Rumsey numbers 1, 2, 7, 42, 429, …

AbstractAndrews's recent proof of the Mills-Robbins-Rumsey conjectured formula for the number of totally symmetric self-complementary plane partitions is used to derive a new multi-variate constant term identity, reminiscent of, but not implied by, Macdonald's BCn-Dyson identity. The method of proof consists in translating to the language of constant terms an expression of Doran for the desired number in terms of sums of minors of a certain matrix. The question of a direct proof of the identity, which would furnish an alternative proof of the Mills-Robbins-Rumsey conjecture, is raised, and a prize is offered for its solution

Multiply-refined enumeration of alternating sign matrices

Four natural boundary statistics and two natural bulk statistics are considered for alternating sign matrices (ASMs). Specifically, these statistics are the positions of the 1's in the first and last rows and columns of an ASM, and the numbers of generalized inversions and -1's in an ASM. Previously-known and related results for the exact enumeration of ASMs with prescribed values of some of these statistics are discussed in detail. A quadratic relation which recursively determines the generating function associated with all six statistics is then obtained. This relation also leads to various new identities satisfied by generating functions associated with fewer than six of the statistics. The derivation of the relation involves combining the Desnanot-Jacobi determinant identity with the Izergin-Korepin formula for the partition function of the six-vertex model with domain-wall boundary conditions.Comment: 62 pages; v3 slightly updated relative to published versio

Alternating sign matrix enumeration involving numbers of inversions and -1's, and positions of boundary 1's

This paper consists of a review of results for the exact enumeration of alternating sign matrices of fixed size with prescribed values of some or all of the following six statistics: the numbers of generalized inversions and -1's, and the positions of the 1's in the first and last rows and columns. Many of these results are expressed in terms of generating functions

2016, UMaine News Press Releases

This is a catalog of press releases put out by the University of Maine Division of Marketing and Communications between January 4, 2016 and December 30, 2016

Divine Domesticities

Divine Domesticities: Christian Paradoxes in Asia and the Pacific fills a huge lacuna in the scholarly literature on missionaries in Asia/Pacific and is transnational history at its finest