Name
Abstract | ||
|---|---|---|
Let X be an algebraic toric set in a projective space over a finite field. We study the vanishing ideal, I(X), of X and show some useful degree bounds for a minimal set of generators of I(X). We give an explicit combinatorial description of a set of generators of I(X), when X is the algebraic toric set associated to an even cycle or to a connected bipartite graph with pairwise vertex disjoint even cycles. In this case, a formula for the regularity of I(X) is given. We show an upper bound for this invariant, when X is associated to a (not necessarily connected) bipartite graph. The upper bound is sharp if the graph is connected. We are able to show a formula for the length of the parameterized linear code associated with any graph, in terms of the number of bipartite and non-bipartite components. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1080/00927872.2012.714025 | COMMUNICATIONS IN ALGEBRA |
Keywords | DocType | Volume |
Lattice ideals,Linear codes,Regularity,Vanishing ideals | Journal | 43 |
Issue | ISSN | Citations |
3 | 0092-7872 | 5 |
PageRank | References | Authors |
0.58 | 6 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jorge Neves | 1 | 7 | 1.24 |
| Maria Vaz Pinto | 2 | 18 | 3.02 |
| Rafael H. Villarreal | 3 | 75 | 15.69 |