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