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:20260404T111137Z UID:T_Seminar/1 DESCRIPTION:Title: Robinson-Schensted correspondence for unit interval orders\nb y Dongkwan Kim (University of Minnesota) as part of T-seminar\n\n\nAbstrac t\nStanley-Stembridge conjecture\, currently one of the most famous conjec tures in algebraic combinatorics\, asks whether a certain generating funct ion with respect to a natural unit interval order is a nonnegative linear combination of complete homogeneous symmetric functions. There are many pa rtial progress on this conjecture\, including its connection with the geom etry of Hessenberg varieties. Here\, instead we study its Schur positivity \, which is originally proved by Haiman and Gasharov. We define an analogu e of Knuth moves with respect to a natural unit interval order and study i ts equivalence classes in terms of D graphs introduced by Assaf. Then\, we show that if the given order avoids certain two suborders then an analogu e of Robinson-Schensted correspondence is well-defined\, which proves that the generating function attached to each equivalence class is Schur posit ive. It is hoped that it proposes a new combinatorial aspect to investigat e the Stanley-Stembridge conjectures and cohomology of Hessenberg varietie s. This work is joint with Pavlo Pylyavskyy.\n LOCATION:https://stable.researchseminars.org/talk/T_Seminar/1/ END:VEVENT END:VCALENDAR