BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Danai Deligeorgaki (KTH Sweden) DTSTART:20250410T120000Z DTEND:20250410T130000Z DTSTAMP:20260423T021333Z UID:GANT/72 DESCRIPTION:Title: Co lored multiset Eulerian polynomials\nby Danai Deligeorgaki (KTH Sweden ) as part of Greek Algebra & Number Theory Seminar\n\n\nAbstract\nThe cent ral objects in this talk are the descent polynomials of colored permutatio ns on multisets\, referred to as colored multiset Eulerian polynomials. Th ese polynomials generalize the colored Eulerian polynomials that appear fr equently in algebraic combinatorics and are known to admit desirable distr ibutional properties\, including real-rootedness\, log-concavity\, unimoda lity and the alternatingly increasing property. In joint work with Bin Han and Liam Solus\, symmetric colored multiset Eulerian polynomials are iden tified and used to prove sufficient conditions for a colored multiset Eule rian polynomial to satisfy the self-interlacing property. This property im plies that the polynomial obtains all of the aforementioned distributional properties as well as others\, including bi-gamma-positivity. To derive t hese results\, multivariate generalizations of a generating function ident ity due to MacMahon are deduced. The results are applied to a pair of ques tions\, both previously studied in several special cases\, that are seen t o admit more general answers when framed in the context of colored multise t Eulerian polynomials. The first question pertains to s-Eulerian polynomi als\, and the second to interpretations of gamma-coefficients. We will see some of these results in detail\, depending on the pace of the talk\n LOCATION:https://researchseminars.org/talk/GANT/72/ END:VEVENT END:VCALENDAR