Braid Parking Varieties

By considering various preimages of projections of a certain braid variety and using the combinatorics of the center of the Hecke algebra, we find (or conjecture) subvarieties whose point counts recover parking numbers, Catalan numbers, HOMFLY coefficients and Kirkman numbers, Kreweras numbers, B-stable ideal numbers, and parabolic parking numbers. The classical combinatorial objects associated to these numbers are obtained from suitable Deodhar decompositions.

For information about the Richard P. Stanley Seminar in Combinatorics, visit https://math.mit.edu/combin/