BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Christian Ikenmeyer (University of Liverpool) DTSTART:20201006T171500Z DTEND:20201006T174500Z DTSTAMP:20260417T205235Z UID:LA-CoCo/4 DESCRIPTION:Title: The Computational Complexity of Plethysm Coefficients\nby Christian Ik enmeyer (University of Liverpool) as part of LA Combinatorics and Complexi ty Seminar\n\n\nAbstract\nWe show that deciding positivity of plethysm coe fficients is NP-hard\, and that computing plethysm coefficients is #P-hard . In fact\, both problems remain hard even if the inner parameter of the p lethysm coefficient is fixed. In this way we obtain an inner versus outer contrast: If the outer parameter of the plethysm coefficient is fixed\, th en the plethysm coefficient can be computed in polynomial time. Moreover\, we derive new lower and upper bounds and in special cases even combinator ial descriptions for plethysm coefficients\, which is a contribution towar ds Stanley's 9th problem from his list from 1999.\n\nOur technique uses di screte tomography in a more refined way than the recent work on Kronecker coefficients by Ikenmeyer\, Mulmuley\, and Walter (2017). This makes our w ork the first to apply techniques from discrete tomography to the study of plethysm coefficients. Quite surprisingly\, that interpretation also lead s to new equalities between certain plethysm coefficients and Kronecker co efficients.\n LOCATION:https://researchseminars.org/talk/LA-CoCo/4/ END:VEVENT END:VCALENDAR