The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers
Journal of Algebraic Combinatorics: An International Journal
Extremal Combinatorics: With Applications in Computer Science
Extremal Combinatorics: With Applications in Computer Science
Algebraic and combinatorial properties of ideals and algebras of uniform clutters of TDI systems
Journal of Combinatorial Optimization
Tight hardness results for minimizing discrepancy
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Relations among conditional probabilities
Journal of Symbolic Computation
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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.