BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dongkwan Kim (University of Minnesota) DTSTART:20200619T070000Z DTEND:20200619T083000Z DTSTAMP:20260422T225823Z UID:T_Seminar/1 DESCRIPTION:Title: Robinson-Schensted correspondence for unit interval orders\nby Dongk wan Kim (University of Minnesota) as part of T-seminar\n\n\nAbstract\nStan ley-Stembridge conjecture\, currently one of the most famous conjectures i n algebraic combinatorics\, asks whether a certain generating function wit h respect to a natural unit interval order is a nonnegative linear combina tion of complete homogeneous symmetric functions. There are many partial p rogress on this conjecture\, including its connection with the geometry of Hessenberg varieties. Here\, instead we study its Schur positivity\, whic h is originally proved by Haiman and Gasharov. We define an analogue of Kn uth moves with respect to a natural unit interval order and study its equi valence classes in terms of D graphs introduced by Assaf. Then\, we show t hat if the given order avoids certain two suborders then an analogue of Ro binson-Schensted correspondence is well-defined\, which proves that the ge nerating function attached to each equivalence class is Schur positive. It is hoped that it proposes a new combinatorial aspect to investigate the S tanley-Stembridge conjectures and cohomology of Hessenberg varieties. This work is joint with Pavlo Pylyavskyy.\n LOCATION:https://researchseminars.org/talk/T_Seminar/1/ END:VEVENT END:VCALENDAR