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Abhyankar’s Recursive Formula Regarding Standard Bi-Tableau

In: Algebraic Geometry and its Applications

Author

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  • Shirinivas G. Udpikar

Abstract

Let X = (X ij ) be an m(l) by m(2) matrix whose entries X ij , 1 ≤ i ≤ m(1), 1 ≤ j ≤ m(2); are indeterminants over a field K. Let K[X] be the polynomial ring in these m(l)m(2) variables over K. In [1], Abhyankar enumerates standard Young bi-tableau with certain conditions and deduces that standard monomials in minors of X form a base for the vector space K[X] over K, a well known result which has been proved by DeConcini-Eisenbud Procesi using straightening formula [2]. The polynomial expression enumerating these bi-tableau involves certain integer valued functions F D (LK) (m, p, a), which characterize the Hilbert polynomial of certain determinantal ideals. Using Abhyankar’s recursive formula developed in [1], we prove certain properties of these integer valued functions.

Suggested Citation

  • Shirinivas G. Udpikar, 1994. "Abhyankar’s Recursive Formula Regarding Standard Bi-Tableau," Springer Books, in: Chandrajit L. Bajaj (ed.), Algebraic Geometry and its Applications, chapter 15, pages 251-259, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2628-4_15
    DOI: 10.1007/978-1-4612-2628-4_15
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