Equi-distribution, cyclic descents, and matchings

Yuval Roichman, Bar Ilan University
Fine Hall 224

In-Person Talk 

The  study of combinatorial parameters of permutations, such as cycle type, inversion number and descent set, may be traced back to Euler.  At the beginning of this talk we will recall some fundamental results in this field, with a focus on the significance of descent sets. We will present examples of existence results and equi-distribution phenomena, whose proofs are algebraic and non-constructive.  A new descent set statistic on involutions, defined geometrically via their interpretation as matchings, will be introduced, and shown to be equi-distributed with the standard one. This concept will be used  to provide an explicit combinatorial construction of cyclic descents on involutions.  No prior knowledge assumed. Based on joint work with Ron Adin.