Roichman, Yuval, Kolokvij junij 2018

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A classical 100 years old result due to MacMahon shows that certain unrelated stastistics are equi-distributed over the symmetric group. It turns out that this result reflects an interesting phenomenon in representation theory, an observation which led to discovery of many new identities on reflection groups. This part is joint with Ron Adin and Francesco Brenti,

Another instance, where graded algebras produce combinatorial identities, is the algebra of quaisymmetric functions. Here we will focus on recent developments with Ron Adin, Ira Gessel and Vic Reiner.

Time allows we will point on intimate relations and applications to positivity problems.

Osebna orodja