2013/04/15 by Hara Charalambous, Charalambous, Hara, Apostolos Thoma +3
Mathematics · #13P10 #14L32 #14M25 #62H17 #Commutative Algebra (math.AC) #FOS: Mathematics #Statistics Theory (math.ST) #math.AC #math.ST #msc:13P10 #msc:14L32 #msc:14M25 #msc:62H17 #stat.TH
paper · pdf · doi:10.48550/arxiv.1304.4257
v3: fixed some typos from v2. The paper will appear in Annals of Combinatorics
arxiv created 2015/10/08 · arxiv updated 2015/10/09
Minimal Markov bases of configurations of integer vectors correspond to minimal binomial generating sets of the assocciated lattice ideal. We give necessary and sufficient conditions for the elements of a minimal Markov basis to be (a) inside the universal Gr" obner basis and (b) inside the Graver basis. We study properties of Markov bases of generalized Lawrence liftings for arbitrary matrices A\inMm× n(ℤ) and B\inMp× n(ℤ) and show that in cases of interest the \em complexity of any two Markov bases is the same.