scholarly journals Minimal generators of toric ideals of graphs

2012 ◽  
Vol 48 (1) ◽  
pp. 64-78 ◽  
Author(s):  
Enrique Reyes ◽  
Christos Tatakis ◽  
Apostolos Thoma
2013 ◽  
Vol 23 (06) ◽  
pp. 1503-1520 ◽  
Author(s):  
ELIZABETH GROSS ◽  
SONJA PETROVIĆ

Associated to any hypergraph is a toric ideal encoding the algebraic relations among its edges. We study these ideals and the combinatorics of their minimal generators, and derive general degree bounds for both uniform and non-uniform hypergraphs in terms of balanced hypergraph bicolorings, separators, and splitting sets. In turn, this provides complexity bounds for algebraic statistical models associated to hypergraphs. As two main applications, we recover a well-known complexity result for Markov bases of arbitrary 3-way tables, and we show that the defining ideal of the tangential variety is generated by quadratics and cubics in cumulant coordinates.


2014 ◽  
Vol 66 (6) ◽  
pp. 1225-1249 ◽  
Author(s):  
Teresa Cortadellas Benítez ◽  
Carlos D'Andrea

AbstractWe exhibit a set of minimal generators of the defining ideal of the Rees Algebra associated with the ideal of three bivariate homogeneous polynomials parametrizing a proper rational curve in projective plane, having a minimal syzygy of degree 2.


2005 ◽  
Vol 40 (6) ◽  
pp. 1361-1382 ◽  
Author(s):  
Karin Gatermann ◽  
Markus Eiswirth ◽  
Anke Sensse

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