Abstract: Plane partitions are classical objects in enumerative and algebraic combinatorics that are in easy bijective correspondence with dimers on the hexagonal grid. Alternating sign matrices, on the other hand, are in easy bijective correspondence with the 6-vertex model from statistical physics. There are classes of plane partitions that are equinumerous with alternating sign matrices or closely related objects, but transparent bijections that would prove these facts seem difficult to construct, which is a mystery to many combinatorialists in this area.
I'll provide an introduction into this area, talk briefly about relations to other areas und present results that have been obtained with various collaborators including Florian Aigner, Arvind Ayyer, Roger Behrend and Matjaz Konvalinka.
A combinatorial perspective on dimers and the $6$-vertex model
14.12.2021 16:45 - 17:45
Organiser:
M. Beiglböck, N. Berestycki, L. Erdös, J. Maas, F. Toninelli
Location:
Zoom Meeting