International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 155-162
On Hilbert polynomial of certain determinantal ideals
Department of Mathematics, S.P. College, Pune 411030, India
Received 2 February 1989; Revised 10 July 1989
Copyright © 1991 Shrinivas G. Udpikar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be an by matrix whose entries , ,
; are indeterminates over a field . Let be the polynomial ring in
these variables over . A part of the second fundamental theorem of
Invariant Theory says that the ideal in , generated by by
minors of is prime. More generally in , Abhyankar defines an ideal in
, generated by different size minors of and not only proves its primeness but
also calculates the Hilbert function as well as the Hilbert polynomial of this
ideal. The said Hilbert polynomial is completely determined by certain integer valued
functions . In this paper we prove some important properties of these
integer valued functions.