Record Details

DSpace at IIT Bombay

View Archive Info
 

Metadata

 
Field Value
 
Title Young bitableaux, lattice paths and Hilbert functions
 
Names GHORPADE, SR (author)
Date Issued 1996 (iso8601)
Abstract A recent result on the enumeration of p-tuples of nonintersecting lattice paths in an integral rectangle is used to deduce a formula of Abhyankar for standard Young bitableaux of certain type, which gives the Hilbert function of a class of determinantal ideals. The lattice path formula is also shown to yield the numerator of the Hilbert series of these determinantal ideals and the h-vectors of the associated simplicial complexes. As a consequence, the a-invariant of these determinantal ideals is obtained in some cases, extending an earlier result of Grabe. Some problems concerning generalizations of these results to 'higher dimensions' are also discussed. In an appendix, the equivalence of Abhyankar's formula for unitableaux of a given shape and a formula of Hedge, obtained in connection with his determination of Hilbert functions of Schubert varieties in Grassmannians, is outlined.
Genre Article; Proceedings Paper
Topic combinatorial
Identifier 0378-3758
Related Item
Related Item