Displaying similar documents to “On Hilbert polynomial of certain determinantal ideals.”

Trajectories of polynomial vector fields and ascending chains of polynomial ideals

Dmitri Novikov, Sergei Yakovenko (1999)

Annales de l'institut Fourier

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We give an explicit upper bound for the number of isolated intersections between an integral curve of a polynomial vector field in ℝ n and an algebraic hypersurface. The answer is polynomial in the height (the magnitude of coefficients) of the equation and the size of the curve in the space-time, with the exponent depending only on the degree and the dimension. The problem turns out to be closely related to finding an explicit upper bound for the length of ascending chains...

Meandering of trajectories of polynomial vector fields in the affine n-space.

Dimitri Novikov, Sergei Yakovenko (1997)

Publicacions Matemàtiques

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We give an explicit upper bound for the number of isolated intersections between an integral curve of a polynomial vector field in Rn and an affine hyperplane. The problem turns out to be closely related to finding an explicit upper bound for the length of ascending chains of polynomial ideals spanned by consecutive derivatives. This exposition constitutes an extended abstract of a forthcoming paper: only the basic steps are outlined here,...

Orderings of monomial ideals

Matthias Aschenbrenner, Wai Yan Pong (2004)

Fundamenta Mathematicae

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We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal invariants for the complexity of this ordered set. In particular, we give an interpretation of the height function in terms of the Hilbert-Samuel polynomial, and we compute bounds on the maximal order type.