BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nancy Wallace (Université du Québec à Montréal) DTSTART:20210426T190000Z DTEND:20210426T200000Z DTSTAMP:20260423T022738Z UID:YUAAS/32 DESCRIPTION:Title: U nexpected relations between parking function formulas\, pattern avoiding p ermutations and the Robinson-Schensted algorithm.\nby Nancy Wallace (U niversité du Québec à Montréal) as part of York University Applied Alg ebra Seminar\n\n\nAbstract\nThe Shuffle theorem of Carlsson and Mellit\, s tates that $\\nabla(e_n)$ is given by parking function formulas. These for mulas are symmetric in the variables q and t. More preciously\, for all n\ , $\\nabla(e_n)$ can be seen as a $GL2×Sn-module$. In this talk we will p ut forth a partial expansion in terms of the irreducible bicharacters of t hese modules. Namely we will expand a subset of the parking function formu las as products of Schur functions in the variables q and t and the usual Schur functions in the variables $X={x1\,x2\,…}$. Part of these formulas are uncovered using a bijection between a subset of paths of area $0$ and standard Young tableaux that sends the dinv statistic to the major index. The Robinson-Schensted algorithm associates a pair of standard Young tabl eaux $(P\,Q)$ to a given permutation. We will end by showing how the previ ous bijection is linked to the $Q$-tableau of some pattern avoiding permut ations that is unrelated to the word of the parking function.\n LOCATION:https://researchseminars.org/talk/YUAAS/32/ END:VEVENT END:VCALENDAR