Christoph Koutschan, Austrian Academy of Sciences

Elaine Wong, Austrian Academy of Sciences

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".

(Note room change)