1,721,007 research outputs found
On the Hilbert quasi-polynomials for non-standard graded rings
Full text linkThe Hilbert function, its generating function and the Hilbert polynomial of a graded ring K[x1, . . . , xk ] have been extensively studied since the famous paper of Hilbert: Ueber die Theorie der algebraischen Formen ([Hilbert, 1890]). In particular, the coefficients and the degree of the Hilbert polynomial play an important role in Algebraic Geometry. If the ring grading is non-standard, then its Hilbert function is not eventually equal to a polynomial but to a quasi-polynomial. It turns out that a Hilbert quasi- polynomial P of degree n splits into a polynomial S of degree n and a lower degree quasi-polynomial T . We have completely determined the degree of T and the first few coefficients of P . Moreover, the quasi-polynomial T has a periodic structure that we have described. We have also developed a software to compute effectively the Hilbert quasi-polynomial for any ring K[x1 , . . . , xk]/I
On the Hilbert quasi-polynomials for non-standard graded rings
No full textThe Hilbert function, its generating function and the Hilbert polynomial of a graded ring K[x1, ..., xk] have been extensively studied since the famous paper of Hilbert: Ueber die Theorie der algebraischen Formen ([Hilbert, 1890]). In particular, the coefficients and the degree of the Hilbert polynomial play an important role in Algebraic Geometry. If the ring grading is non-standard, then its Hilbert function is not eventually equal to a polynomial but to a quasi-polynomial. It turns out that a Hilbert quasi-polynomial P of degree n splits into a polynomial S of degree n and a lower degree quasi-polynomial T. We have completely determined the degree of T and the first few coefficients of P. Moreover, the quasi-polynomial T has a periodic structure that we have described. We have also developed a software to compute effectively the Hilbert quasi-polynomial for any ring K[x1, ..., xk]/I
ODD-CYCLE-FREE FACET COMPLEXES AND THE KONIG PROPERTY
No full textFacet complexes and simplicial cycles were introduced to help study the interplay between graph theoretical and algebraic properties of hypergraphs. We use the definition of a simplicial cycle to define an odd-cycle-free facet complex (hypergraph). These are facet complexes that do not contain any cycles of odd length. We show that, besides one class of such facet complexes, all of them satisfy the Konig property. This new family of complexes includes the family of balanced hypergraphs, which are known to satisfy the Konig property. These odd-cycle-free facet complexes are, however, not necessarily Mengerian. Copyright © 2011 Rocky Mountain Mathematics Consortium
Reducing the size and number of linear programs in a dynamic Gröbner basis algorithm (Preprint)
No full textPreprint su arXi
Group Action on Groebner Bases of Saturated Zero-Dimensional Binomial Ideals
No full textFully saturated zero-dimensional binomial ideals (lattice ideals) describe
lattices on Zn that are of interest in cryptanalysis. Gr ̈obner basis
computation for these ideals are computationally very intensive. We
sketch a modified version of Buchberger’s algorithm for lattice ideals that
are closed with respect to a group action on their indeterminates. The
main idea is to exploit the symmetries of such ideals to avoid performing
S-polynomial reductions that are “equivalent” with respect to the group
action. Using our techniques the number of S-polynomials to be considered
can be reduced by a factor up to the order of the grou
The Chen-Reed-Helleseth-Truong Decoding Algorithm and the Gianni-Kalkbrenner Groebner Shape Theorem
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