Generalized cover ideals and the persistence property |
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Authors: | Ashwini Bhat Jennifer Biermann Adam Van Tuyl |
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Affiliation: | 1. Department of Mathematics, Oklahoma State University, 401 Mathematical Sciences, Stillwater, OK 74078, USA;2. Department of Mathematics and Statistics, 451A Clapp Lab, Mount Holyoke College, South Hadley, MA 01075, USA;3. Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON P7B 5E1, Canada |
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Abstract: | Let I be a square-free monomial ideal in R=k[x1,…,xn], and consider the sets of associated primes Ass(Is) for all integers s?1. Although it is known that the sets of associated primes of powers of I eventually stabilize, there are few results about the power at which this stabilization occurs (known as the index of stability). We introduce a family of square-free monomial ideals that can be associated to a finite simple graph G that generalizes the cover ideal construction. When G is a tree, we explicitly determine Ass(Is) for all s?1. As consequences, not only can we compute the index of stability, we can also show that this family of ideals has the persistence property. |
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Keywords: | 13F20 13A15 05C25 |
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