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Algebraic properties of ideals of poset homomorphisms

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Abstract

Given finite posets P and Q, we consider a specific ideal L(P, Q), whose minimal monomial generators correspond to order-preserving maps \(\phi :P\rightarrow Q\). We study algebraic invariants of those ideals. In particular, sharp lower and upper bounds for the Castelnuovo–Mumford regularity and the projective dimension are provided. We obtain precise formulas for a large subclass of these ideals. Moreover, we provide complete characterizations for several algebraic properties of L(P, Q), including being Buchsbaum, Cohen–Macaulay, Gorenstein, Golod and having a linear resolution.

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Notes

  1. After the present paper appeared on the arXiv, this problem was solved by D’Alì, Fløystad and Nematbakhsh in [3].

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Authors and Affiliations

  1. Institut für Mathematik, Universität Osnabrück, 49069, Osnabrück, Germany

    Martina Juhnke-Kubitzke & Sara Saeedi Madani

  2. Institut für Mathematik, Goethe-Universität Frankfurt, 60054, Frankfurt am Main, Germany

    Lukas Katthän

Authors
  1. Martina Juhnke-Kubitzke
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  2. Lukas Katthän
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  3. Sara Saeedi Madani
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Correspondence to Lukas Katthän.

Additional information

Martina Juhnke-Kubitzke and Sara Saeedi Madani were supported by the German Research Council DFG-GRK 1916.

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Juhnke-Kubitzke, M., Katthän, L. & Saeedi Madani, S. Algebraic properties of ideals of poset homomorphisms. J Algebr Comb 44, 757–784 (2016). https://doi.org/10.1007/s10801-016-0687-5

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  • DOI: https://doi.org/10.1007/s10801-016-0687-5

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