Markov complexity of monomial curves

作者：Charalambous Hara; Thoma Apostolos; Vladoiu Marius^*

来源：Journal of Algebra, 2014, 417: 391-411.

DOI：10.1016/j.jalgebra.2014.06.025

• Toric ideals
• Markov basis
• Graver basis
• Lawrence liftings

Let A = {a(1),...,a(n)} subset of N-m. We give an algebraic characterization of the universal Markov basis of the toric ideal I-A. We show that the Markov complexity of A = {n(1), n(2), n(3)} is equal to 2 if I-A is complete intersection and equal to 3 otherwise, answering a question posed by Santos and Sturmfels. We prove that for any r %26gt;= 2 there is a unique minimal Markov basis of A((r)). Moreover, we prove that for any integer l there exist integers n(1), n(2), n(3) such that the Graver complexity of A is greater than l.

• 出版日期2014-11-1