scholarly journals Minimal generators of toric ideals of graphs

2012 ◽  
Vol 48 (1) ◽  
pp. 64-78 ◽  
Author(s):  
Enrique Reyes ◽  
Christos Tatakis ◽  
Apostolos Thoma
Keyword(s):  
Toric Ideals ◽  
Minimal Generators

scholarly journals COMBINATORIAL DEGREE BOUND FOR TORIC IDEALS OF HYPERGRAPHS

2013 ◽  
Vol 23 (06) ◽  
pp. 1503-1520 ◽  
Author(s):  
ELIZABETH GROSS ◽  
SONJA PETROVIĆ
Keyword(s):  
Statistical Models ◽  
Toric Ideals ◽  
Toric Ideal ◽  
Complexity Bounds ◽  
Markov Bases ◽  
Uniform Hypergraphs ◽  
Degree Bounds ◽  
Complexity Result ◽  
Minimal Generators ◽  
Degree Bound

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.

Minimal Generators of the Defining Ideal of the Rees Algebra Associated with a Rational Plane Parametrization with μ = 2

2014 ◽  
Vol 66 (6) ◽  
pp. 1225-1249 ◽  
Author(s):  
Teresa Cortadellas Benítez ◽  
Carlos D'Andrea
Keyword(s):  
Projective Plane ◽  
Rational Curve ◽  
Rees Algebra ◽  
Homogeneous Polynomials ◽  
Rational Plane ◽  
Minimal Generators ◽  
The Ideal

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.

scholarly journals Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems

2005 ◽  
Vol 40 (6) ◽  
pp. 1361-1382 ◽  
Author(s):  
Karin Gatermann ◽  
Markus Eiswirth ◽  
Anke Sensse
Keyword(s):  
Graph Theory ◽  
Mass Action ◽  
Hopf Bifurcations ◽  
Toric Ideals ◽  
Action Systems
Sign in / Sign up

Export Citation Format

Share Document