Ju l 2 00 1 BOUNDS FOR BETTI NUMBERS
نویسنده
چکیده
In this paper we prove parts of a conjecture of Herzog giving lower bounds on the rank of the free modules appearing in the linear strand of a graded k-th syzygy module over the polynomial ring. If in addition the module is Z n-graded we show that the conjecture holds in full generality. Furthermore, we give lower and upper bounds for the graded Betti numbers of graded ideals with a linear resolution and a fixed number of generators.
منابع مشابه
ar X iv : 0 80 7 . 21 85 v 1 [ m at h . A C ] 1 4 Ju l 2 00 8 SPLITTINGS OF MONOMIAL IDEALS
We provide some new conditions under which the graded Betti numbers of a mono-mial ideal can be computed in terms of the graded Betti numbers of smaller ideals, thus complementing Eliahou and Kervaire's splitting approach. As applications, we show that edge ideals of graphs are splittable, and we provide an iterative method for computing the Betti numbers of the cover ideals of Cohen-Macaulay b...
متن کامل[ m at h . Q A ] 1 5 O ct 2 00 4 ON RACK COHOMOLOGY
We prove that the lower bounds for Betti numbers of the rack, quandle and degeneracy cohomol-ogy given in [CJKS] are in fact equalities. We compute as well the Betti numbers of the twisted cohomology introduced in [CES]. We also give a group-theoretical interpretation of the second cohomology group for racks.
متن کاملUpper Bounds for Betti Numbers of Multigraded Modules
This paper gives a sharp upper bound for the Betti numbers of a finitely generated multigraded R-module, where R = k[x1, . . . , xm] is the polynomial ring over a field k in m variables. The bound is given in terms of the rank and the first two Betti numbers of the module. An example is given which achieves these bounds simultaneously in each homological degree. Using Alexander duality, a bound...
متن کامل. A C ] 1 7 Ju l 2 00 3 DISTRIBUTIVE LATTICES , BIPARTITE GRAPHS AND ALEXANDER DUALITY
A certain squarefree monomial ideal HP arising from a finite partially ordered set P will be studied from viewpoints of both commutative algebra and combinatorics. First, it is proved that the defining ideal of the Rees algebra of HP possesses a quadratic Gröbner basis. Thus in particular all powers of HP have linear resolutions. Second, the minimal free graded resolution of HP will be construc...
متن کاملar X iv : m at h / 06 06 73 4 v 1 [ m at h . M G ] 2 8 Ju n 20 06 CODES IN SPHERICAL CAPS
We consider bounds on codes in spherical caps and related problems in geometry and coding theory. An extension of the Delsarte method is presented that relates upper bounds on the size of spherical codes to upper bounds on codes in caps. Several new upper bounds on codes in caps are derived. Applications of these bounds to estimates of the kissing numbers and one-sided kissing numbers are consi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001