Algebraic properties of classes of path ideals of posets |
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Authors: | Martina Kubitzke Anda Olteanu |
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Institution: | 1. FB 12 – Institut für Mathematik, Goethe-Universität, Robert-Mayer-Straße 10, D-60325 Frankfurt am Main, Germany;2. University Politehnica of Bucharest, Faculty of Applied Sciences, Splaiul Independen?ei, No. 313, 060042, Bucharest, Romania;3. Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Group of the Project PD-3-0235, P.O. Box 1-764, Bucharest 014700, Romania |
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Abstract: | We consider path ideals associated to special classes of posets such as tree posets and cycles. We express their property of being sequentially Cohen–Macaulay in terms of the underlying poset. Moreover, monomial ideals, which arise in algebraic statistics from the Luce-decomposable model and the ascending model, can be viewed as path ideals of certain posets. We study invariants of these so-called Luce-decomposable monomial ideals and ascending ideals for diamond posets and products of chains. In particular, for these classes of posets, we explicitly compute their Krull dimension, their projective dimension, their Castelnuovo–Mumford regularity and their Betti numbers. |
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Keywords: | 13F55 13C15 13C14 |
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