Matchings in simplicial complexes, circuits and toric varieties
The authors introduced a generalized notion of matching in a simplicial complex, called \(J\)-matching, and use it to define certain combinatorial invariants of the complex. Recently in [\textit{A. Katsabekis, M. Morales} and \textit{A. Thoma}, J. Pure Appl. Algebra 204, No. 3, 584--601 (2006; Zbl 1094.13035)], to any lattice ideal it was associated a cone \(\sigma \) and a simplicial complex \(D_\sigma \), with vertices the minimal non faces of \(\sigma \), as it was shown there combinatorial invariants of \(D_\sigma \) provides bounds for the minimal number of equations needed to described set theoretically an algebraic set: \(\text{ara}(V)\). The main object of the paper under review consists in giving lower bounds for \(\text{ara}(V)\) in terms of matching and other combinatorial numbers, for this the authors study first the properties of the generalized notion of matching.
scientific article; zbMATH DE number 5129733