We prove that many families of toric ideals stabilize up to symmetry. Our results imply Hillar-Sullivant's Independent Set Theorem and settle afformatively questions in work by Aschenbrenner-Hillar, Hillar-Sullivant, and Hillar-Martin del Campo. Our approach involves splitting an equivariant monomial map into a part for which we have an explicit degree bound of the kernel, and a part for which we can prove that the source, a so-called matching monoid, is equivariantly Noetherian.

Original language | English |
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Publisher | s.n. |
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Number of pages | 20 |
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Publication status | Published - 2013 |
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Name | arXiv.org |
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Volume | 1306.0828 [math.AC] |
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