BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Russell Hendel (Towson University) DTSTART:20260717T190000Z DTEND:20260717T192500Z DTSTAMP:20260710T111434Z UID:CANT2026/71 DESCRIPTION:Title: Improvements in calculating the recursion satisfied by a family of deter minants\nby Russell Hendel (Towson University) as part of Combinatoria l and additive number theory seminar (CANT 2026)\n\nLecture held in Scienc e Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nA variety o f problems can be elegantly solved by identifying the recursion satisfied by the determinants of a family of matrices. In 2016\, Jia\, Yang\, and Li provided a general 6-th order recursion for the family of arbitrary pentd iagonal Toeplitz matrices by using Laplace expansions. Recently\, Evans an d Hendel showed that this method is potentially generalizable and applied it to prove an outstanding conjecture on resistance distance in linear 3-t rees. However\, Evans and Hendel left as an open problem the convergence o f their procedure in the general case. Hendel has recently proven converge nce for such a Laplace-expansion approach for an arbitrary family of squar e\, banded\, Toeplitz matrices with $k$ super and sub diagonals for any po sitive integer $k.$ Hendel also eliminated the computational matrix method s of Evans and Hendel replacing them with a simpler algebraic manipulative system. This note supplements this procedure by showing an improved metho d to solve the resulting system of several simultaneous equations in famil ies of determinants. This improved procedure\, applied to explore an outst anding conjecture of Bareett\, Evans\, and Francis on the general $k$-line ar tree\, uncovers several interesting patterns which are presented.\n LOCATION:https://researchseminars.org/talk/CANT2026/71/ END:VEVENT END:VCALENDAR