DATE2023-05-18 15:10-16:00

PLACE數學系館 1F3174教室

SPEAKER李宜霖 博士(Indiana University

TITLEAn Extension of the Lindstrom--Gessel--Viennot Theorem

ABSTRACT In this talk, I will introduce the Lindstr?m--Gessel--Viennot theorem and our extension and present some applications and open problems. The Lindstr?m--Gessel--Viennot theorem is a powerful and elegant result with numerous applications in different contexts, such as enumerating various types of plane partitions, semi-standard Young tableaux, and providing combinatorial proof of the Jacobi--Trudi type identities and some determinant formulas. This theorem gives a determinant formula for the signed enumeration of families of non-intersecting paths with any given starting and ending points (according to the connection type). Our result provides the straight count of these families, expressing it as a determinant whose entries are signed counts of lattice paths with given starting and ending points.