NDLI: Toric algebra of hypergraphs

Content Provider	Springer Nature Link
Author	Petrović, Sonja Stasi, Despina
Copyright Year	2013
Abstract	The edges of any hypergraph parametrize a monomial algebra called the edge subring of the hypergraph. We study presentation ideals of these edge subrings, and describe their generators in terms of balanced walks on hypergraphs. Our results generalize those for the defining ideals of edge subrings of graphs, which are well-known in the commutative algebra community, and popular in the algebraic statistics community. One of the motivations for studying toric ideals of hypergraphs comes from algebraic statistics, where generators of the toric ideal give a basis for random walks on fibers of the statistical model specified by the hypergraph. Further, understanding the structure of the generators gives insight into the model geometry.
Starting Page	187
Ending Page	208
Page Count	22
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	39
Issue Number	1
e-ISSN	15729192
Language	English
Publisher	Springer US
Publisher Date	2013-04-20
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hypergraph Edge ring Markov basis Toric ideal Monomial walk Sunflower Combinatorial discrepancy Parameter hypergraph Combinatorics Convex and Discrete Geometry Order, Lattices, Ordered Algebraic Structures Computer Science Group Theory and Generalizations
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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Toric algebra of hypergraphs