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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/100/1162

Title: Young bitableaux, lattice paths and Hilbert functions
Authors: GHORPADE, SR
Keywords: combinatorial
Issue Date: 1996
Publisher: ELSEVIER SCIENCE BV
Citation: JOURNAL OF STATISTICAL PLANNING AND INFERENCE,54(1)55-66
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.
URI: http://dx.doi.org/10.1016/0378-3758(95)00156-5
http://dspace.library.iitb.ac.in/xmlui/handle/10054/14358
http://hdl.handle.net/100/1162
ISSN: 0378-3758
Appears in Collections:Proceedings papers

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