# Ilse Fischer: Alternating sign trapezoids and cyclically symmetric lozenge tilings with a central hole

**Time: **
Wed 2020-01-29 10.30 - 11.20

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan

**Lecturer: **
Ilse Fischer, University of Vienna

### Abstract

For about 35 years now, combinatorialists have tried to find bijections between three classes of objects that are all counted by the product formula \(\prod\limits_{i=0}^{n-1} \frac{(3i+1)!}{(n+i)!}\).

These objects are \(n \times n\) alternating sign matrices, totally symmetric self-complementary plane partitions in a \(2n \times 2n \times 2n\) box, and descending plane partitions with parts at most \(n\). Recently, we have added a fourth class of objects to this list, namely alternating sign triangles, and, even more recently, we have extended this class to alternating sign trapezoids, and have shown that they are equinumerous with cyclically symmetric lozenge tilings tilings of a hexagon with a central hole of size \(k\). Partly based on joint work with Arvind Ayyer and Roger Behrend