Abstract
The support poset of a monomial ideal \(I\subseteq {{\mathbf {k}}}[x_1,\ldots ,x_n]\) encodes the relation between the variables \(x_1,\ldots ,x_n\) and the minimal monomial generators of I. It is known that not every poset is realizable as the support poset of some monomial ideal. We describe some posets P for which we can explicitly find at least one monomial ideal \(I_P\) such that P is the support poset of \(I_P\). Also, for some families of monomial ideals we describe their support posets and study their properties. As an example of application we examine the relation between forests and series-parallel ideals.
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Notes
If \(i=1\) then take m instead of \(i-1\), and if \(i=m\) take 1 instead of \(i+1\).
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Acknowledgements
The authors are partially funded by grant MTM2017-88804-P of Ministerio de Economía, Industria y Competitividad (Spain). The first cited author is partially funded by University of La Rioja predoctoral (education) researcher Grant on 2018.
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Pascual-Ortigosa, P., Sáenz-de-Cabezón, E. Support posets of some monomial ideals. AAECC 33, 457–475 (2022). https://doi.org/10.1007/s00200-020-00461-9
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DOI: https://doi.org/10.1007/s00200-020-00461-9