School Seminars and Colloquia

Proof of the alternating sign matrix and descending plane partition conjecture

Mathematical Physics Seminar

by Roger Behrend

Institution: Cardiff University
Date: Mon 16th May 2011
Time: 1:00 PM
Location: Old Geology 2, The University of Melbourne

Abstract: : Alternating sign matrices (ASMs) and descending plane partitions (DPPs)are combinatorial objects, each of which arose about 30 years ago, but in very different contexts. However, it was conjectured by Mills, Robbins and Rumsey in 1983 that certain finite sets of ASMs have the same sizes as certain finite sets of DPPs, where these sets are comprised of all ASMs or DPPs with fixed values of particular statistics. In this talk, a proof of this conjecture will be presented.
The proof will involve various standard results and techniques: a bijection between ASMs and configurations of the six-vertex model with domain-wall boundary conditions, the Izergin-Korepin determinant formula, a bijection between DPPs and certain sets of nonintersecting lattice paths, the Lindstrom-Gessel-Viennot theorem, and elementary transformations of determinants using generating functions.

This is joint work with Philippe Di Francesco and Paul Zinn-Justin.
Full details appear in arXiv:1103.1176.

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