Seminar Details
Symbolic Evaluation of Determinants and Rhombus Tilings of Holey Hexagons
- Start Date: July 20, 2018
- Event Start Time: 4:00 PM
- Event End Time: 4:45 PM
- Seminar Series: Experimental Math Seminar
- Presenter(s): Elaine Wong - Austrian Academy of Sciences || Christoph Koutschan - Austrian Academy of Sciences
- Event Location: Hill Center- Room 525 | Rutgers University
- Event Additional Info: <p><strong>(Note room change) </strong></p>
- Presentation Type: Stand Alone Presentation
- Abstract:
We investigate a curious determinant that was first mentioned by George Andrews in 1980 in the context of descending plane partitions. It is found to be a special instance of a two-parameter family of determinants that count certain collections of nonintersecting lattice paths, or, equivalently, cyclically symmetric rhombus tilings of a hexagon with several triangular holes inside. We find closed forms for several one-parameter subfamilies, both by applying combinatorial arguments and by applying Zeilberger's "holonomic ansatz".