Minimal generating sets of lattice ideals

• Autores: Hara Charalambous, Apostolos Thoma, Marius Vladoiu
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 68, Fasc. 3, 2017, págs. 377-400
• Idioma: inglés
• DOI: 10.1007/s13348-017-0191-9
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• Resumen

  • Let L\subset \mathbb {Z}^n be a lattice and I_L=\langle x^{\mathbf {u}}-x^{\mathbf {v}}:\ {\mathbf {u}}-{\mathbf {v}}\in L\rangle be the corresponding lattice ideal in \Bbbk [x_1,\ldots , x_n], where \Bbbk is a field. In this paper we describe minimal binomial generating sets of I_L and their invariants. We use as a main tool a graph construction on equivalence classes of fibers of I_L. As one application of the theory developed we characterize binomial complete intersection lattice ideals, a longstanding open problem in the case of non-positive lattices.