Finite Groebner bases in infinite dimensional polynomial rings and applications
By Christopher J. Hillar, Seth Sullivant. 2009
115 citations recorded by the source corpus.
We introduce the theory of monoidal Groebner bases, a concept which generalizes the familiar notion in a polynomial ring and allows for a description of Groebner bases of ideals that are stable under the action of a monoid. The main motivation for developing this theory is to prove finiteness theorems in commutative algebra and its applications. A major result of this type is that ideals in infinitely many indeterminates stable under the action of the symmetric group are finitely generated up to symmetry. We use this machinery to give new proofs of some classical finiteness theorems in algebraic statistics as well as a proof of the independent set conjecture of Hosten and the second author.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/51c8a02b8e35b4ba264343c04e9aedeff3e5c7db
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- Noetherianity up to Symmetry (2013, unknown): “We formulate and prove the independent set theorem from [ HS12 ], first conjectured in [ SHS07 ], directly at the level of ideals.”
- FI- and OI-modules with varying coefficients (2017, background): “Using the above arguments and the results in [14], it also follows that the tensor products (X) and (X) are noetherian for every c ∈ N.”
- Arc Spaces and Rogers-Ramanujan Identities (2011, unknown): “Connecting both ideas will demand handling Gröbner basis in countably many variables, a problem which has been successfully dealt with in different contexts over the last years (see Hillar and Sullivant (2009), Draisma (2010)).”