BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Catherine Yan (Texas A&M University) DTSTART:20220525T200000Z DTEND:20220525T202500Z DTSTAMP:20260423T011340Z UID:CANT2022/28 DESCRIPTION:Title: Multivariate Goncarov polynomials and integer sequences\nby Catheri ne Yan (Texas A&M University) as part of Combinatorial and additive number theory (CANT 2022)\n\n\nAbstract\nUnivariate delta Gon\\v{c}arov polynomi als arise when the classical Gon\\v{c}arov interpolation problem in numeri cal analysis is modified by replacing derivatives with delta operators. Wh en the delta operator under consideration is the backward difference opera tor\, we acquire the univariate difference Gon\\v{c}arov polynomials\, whi ch have a combinatorial relation to lattice paths in the plane with a give n right boundary. In this talk\, we extend several algebraic and analytic properties of univariate Gon\\v{c}arov polynomials to the multivariate ca se with both the derivative and backward difference operators. We then est ablish a combinatorial interpretation of multivariate Gon\\v{c}arov polyn omials in terms of certain constraints on $d$-tuples of integer sequences. This motivates a connection between multivariate Gon\\v{c}arov polynomia ls and a higher-dimensional generalized parking function\, the $\\mathbf{U }$-parking function\, from which we derive several enumerative results bas ed on the theory of delta operators. \n\nThis talk is based on joint wor k with Ayo Adeniran and Lauren Snider.\n LOCATION:https://researchseminars.org/talk/CANT2022/28/ END:VEVENT END:VCALENDAR