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Showing 1 to 10 of 10 for “"Hilbert Function"”.
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Maximum Betti Numbers for a Given Hilbert Function
… gave a necessary and sufficient condition for a function H to be the Hilbert function of a cyclic module over a polynomial ring $R = k\lbrack x\sb1,\..., x\sb{n}\rbrack$ where k is a field of characteristic 0. He constructed the lex-segment ideal which has a given Hilbert function through degree …
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Monomial Ideals, N-Lists, and Smallest Graded Betti Numbers
… smallest graded betti numbers. Given an Artinian Hilbert function H , consider all ideals I ⊂ R such that H(R/I) = H . Then the graded betti numbers which correspond to these ideals form a finite set which we partially order component-wise. It is known that this set has a largest element, but …
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The maximal rank conjecture
… Maximal Rank Conjecture, which determines the Hilbert function of C Pr.
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Homological invariants of some special varieties
… invariants (e.g., graded Betti numbers, Hilbert function, regularity) of some special varieties. In particular, we focus on the codimension two ACM varieties in P1×P1×P1 (called varieties of lines), and the edge ideals of bicyclic graphs. We study the Hilbert function of Ferrers varieties …
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Irrational behavior of algebraic discrete valuations
… discrete rank 1 valuations whose associated Hilbert function cannot be written as the sum of a quasi-polynomial and a bounded function. We further show that the set of multiplicities associated to these algebraic discrete rank 1 valuations contains the interval [0, 1/8 ). In particular, the …
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Algebraic methods in pseudorandomness and circuit complexity
… construction. We exhibit a collection of natural functions that behave pseudorandomly with regards to AC⁰ tests. We also exactly determine the F₂-polynomial degree of the recursive Fourier sampling problem and use this to provide new partial results towards a circuit lower bound for this problem. …
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Symbolic-numeric algorithms for simplifying differential systems and their application to the determination of approximate Lie symmetry algebras
… the approximate subsystem and the differential Hilbert function of the exact subsystem. This approach enhances the efficiency in simplifying PDE systems involving both exact and approximate parameters. Another contribution of this thesis is the establishment of a foundation for constructing and …
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Combinatorics related to the totally nonnegative Grassmannian
… O-sequence, which is a sequence coming froi a Hilbert function of a monomial Artinian level algebra. We show that the conjecture holds for positroids: that is, the h-vector of a positroid is a pure O-sequence.
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An Introduction to Fröberg's Conjecture
<p>The goal of this thesis is to make Fröberg's conjecture more accessible to the average math graduate student by building up the necessary background material to understand specific examples where Fröberg's conjecture is true.</p>
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Zero-dimensional schemes: curves, singularities and tensors
L'abstract è presente nell'allegato / the abstract is in the attachment