[Fall 1998
Colloquiums]
[Department Homepage]
DEPARTMENT OF MATHEMATICS AND STATISTICS
OAKLAND UNIVERSITY
ROCHESTER, MICHIGAN 48309
Devadatta Kulkarni
Department of Mathematics and Statistics
Oakland University
The Hilbert Polynomial of a
Ladder Determinantal Ideal
Abstract
In this talk we survey the results over the past thirteen years in the area of finding the Hilbert polynomial of a ladder determinantal ideal. Hilbertianness of these ideals was shown by Abhyankar and Kulkarni (1988). The first explicit formula for counting paths lying above a fixed path having a given number of corners due to Kulkarni (1985) remains at the heart of all major results in this area. These investigations bring out very rich interplay between algebra and combinatorics. Conca and Herzog conjectured a determinantal formula for the Hilbert function of a one-sided ladder determinantal ideal in 1994. Krattenthaler and Prohosca (1997) provided a combinatorial proof. We also present an outline of an alternative proof of Conca-Herzog's conjecture using Gessel-Viennot switching of paths. This is a joint work with Ian P. Goulden.
372 Science and Engineering Building
Tuesday, September 29, 1998
3:004:00 P.M.
Refreshments at 2:303:00 P.M. in Room 368, Science and Engineering Building