Let I(G) be the edge ideal associated to a simple graph G. We study the graded Betti numbers that appear in the linear strand of the minimal free resolution of I(G).

This paper is concerned with the problem of determining up to graded isomorphism the modules in a minimal free resolution of a fat point subscheme Z = m1p1 + · · ·+ mrpr ⊂ P 2 for general points p1, . . . , pr.

Let I(G) be the edge ideal associated to a simple graph G. We study the graded Betti numbers that appear in the linear strand of the minimal free resolution of I(G).

Alter Breath-hold duration Increasing parallel-imaging factors (up to x 4 routinely) will reduce breath-hold with minimal impact on SSFP quality. Reduce spatial resolution small reductions in phase resolution will significantly reduce breath-hold Increasing the echo train/segments shorten breathhold, with slight decrease in temporal resolution Increase the number of averages(3-5) for free-breat...

The Koszul homology of modules of the polynomial ring R is a central object in commutative algebra. It is strongly related with the minimal free resolution of these modules, and thus with regularity, Hilbert functions, etc. Here we consider the case of modules of the form R/I where I is a monomial ideal. So far, some good algorithms have been given in the literature and implemented in different...

Let k an algebraically closed field, P the n-dimensional projective space over k and TPn the tangent vector bundle of P . In this paper I prove the following result : for every integer l, for every non-negative integer s, if Zs is the union of s points in sufficiently general position in P, then the restriction map H(P, TPn(l)) → H 0(Zs, TPn(l)|Zs) has maximal rank. This result implies that the...

Abstract We give an explicit minimal graded free resolution, in terms of representations the symmetric group S d {S_{d}} , a Galois-theoretic configuration d points

A graph G is a minimal claw-free graph (m.c.f. graph) if it contains no K1,3 (claw) as an induced subgraph and if, for each edge e of G, G − e contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices, and characterize graphs which have m.c.f. line graphs. MSC 2000: 05C75, 05C07