2012/06/12 by Elizabeth Gross, Gross, Elizabeth, Sonja Petrović +1 · 3 citations
Computer Science · Mathematics · #Algebraic number #Combinatorics #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #Degree (music) #Discrete mathematics #FOS: Mathematics #Hypergraph #Ideal (ethics) #Markov chain #Mathematics #Polynomial and algebraic computation #Tensor decomposition and applications #Variety (cybernetics) #math.AC #math.CO
paper · pdf · doi:10.48550/arxiv.1206.2512
published in arXiv (Cornell University) (Cornell University) · Revised, improved, reorganized. We recommend viewing figures in color
openalex publication_date 2012/06/12 · arxiv created 2012/12/21 · arxiv updated 2012/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.