graver basis
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2019 ◽  
Vol 10 (1) ◽  
pp. 128-136 ◽  
Author(s):  
Seth Sullivant

A homogeneous ideal is robust if its universal Gröbner basis is also a minimal generating set.  For toric ideals, one has the stronger definition: A toric ideal is strongly robust if its Graver basis equals the set of indispensable binomials.  We characterize the codimension 2  strongly robust toric ideals by their Gale diagrams.  This give a positive answer to a question of Petrovic, Thoma, and Vladoiu in the case of codimension 2 toric ideals.



10.37236/5912 ◽  
2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Mourtadha Badiane ◽  
Isaac Burke ◽  
Emil Sköldberg

We show that the universal Gröbner basis and the Graver basis of a binomial edge ideal coincide. We provide a description for this basis set in terms of certain paths in the underlying graph. We conjecture a similar result for a parity binomial edge ideal and prove this conjecture for the case when the underlying graph is the complete graph.



2015 ◽  
Vol 6 (1) ◽  
Author(s):  
Raymond Hemmecke ◽  
Tobias Windisch

We consider the connectivity of fiber graphs with respect to Gro ̈bner basis and Graver basis moves. First, we present a sequence of fiber graphs using moves from a Gro ̈bner basis and prove that their edge-connectivity is lowest possible and can have an arbitrarily large distance from the minimal degree. We then show that graph-theoretic properties of fiber graphs do not depend on the size of the right-hand side. This provides a counterexample to a conjecture of Engstro ̈m on the node-connectivity of fiber graphs. Our main result shows that the edge-connectivity in all fiber graphs of this counterexample is best possible if we use moves from Graver basis instead. 



2013 ◽  
Vol 145 (1-2) ◽  
pp. 1-18 ◽  
Author(s):  
Raymond Hemmecke ◽  
Matthias Köppe ◽  
Robert Weismantel


2012 ◽  
Vol 65 (1) ◽  
pp. 191-212 ◽  
Author(s):  
Mitsunori Ogawa ◽  
Hisayuki Hara ◽  
Akimichi Takemura


2012 ◽  
Vol 6 (2) ◽  
pp. 147-165 ◽  
Author(s):  
Irene Márquez-Corbella ◽  
Edgar Martínez-Moro
Keyword(s):  


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