Lattice structures of Gog and Magog triangles
Time: 14:00 -- Location: LRI, 445
summary:
Gog and Magog triangles are simple combinatorial objects which are equienumerated.
Howewer, the problem of finding an explicit bijection between these has been an
open problem since the 80’s. These are related to other interesting objects such
as alternating sign matrices, plane partitions or aztec diamond tillings.
All these objects can be ordered in such a way that the obtained posets are distributive
lattices. We will present Gog and Magog triangles under a lattice-theoretic point of
view, giving new explanations of the link between alternating sign matrices and aztec
diamond tillings, or between the lattice of Gog triangles, the Bruhat and weak orders
on permutations.