Acta Mathematica Vietnamica

, Volume 44, Issue 1, pp 213–241 | Cite as

Poset Ideals of P-Partitions and Generalized Letterplace and Determinantal Ideals

  • Gunnar FløystadEmail author


For any finite poset P, we have the poset of isotone maps \(\text {Hom}(P,\mathbb {N})\), also called \(P^{\text {op}}\)-partitions. To any poset ideal \(\mathcal {J}\) in \(\text {Hom}(P,\mathbb {N})\), finite or infinite, we associate monomial ideals: the letterplace ideal \(L(\mathcal {J},P)\) and the Alexander dual co-letterplace ideal \(L(P,\mathcal {J})\), and study them. We derive a class of monomial ideals in \(\Bbbk [x_{p}, p \in P]\) called P-stable. When P is a chain, we establish a duality on strongly stable ideals. We study the case when \(\mathcal {J}\) is a principal poset ideal. When P is a chain, we construct a new class of determinantal ideals which generalizes ideals of maximal minors and whose initial ideals are letterplace ideals of principal poset ideals.


Poset ideals Letterplace ideals P-partitions Strongly stable ideals Determinantal ideals 

Mathematics Subject Classification (2010)

Primary 13F55, 05E40 Secondary 13C40, 14M12 


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Matematisk InstituttUniversitetet i BergenBergenNorway

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