Poset ideals of P-partitions and generalized letterplace and determinantal ideals
| Autor: | Gunnar Fløystad |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Class (set theory)
Monomial 021103 operations research Mathematics::Commutative Algebra General Mathematics Isotone 010102 general mathematics 0211 other engineering and technologies Duality (order theory) 02 engineering and technology Commutative Algebra (math.AC) Mathematics - Commutative Algebra 01 natural sciences 13F55 05E40 (Primary) 13C40 14M12 (Secondary) Combinatorics FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) Ideal (ring theory) 0101 mathematics Partially ordered set Mathematics |
| Popis: | For any finite poset $P$ we have the poset of isotone maps $\text{Hom}(P,\mathbb{N})$, also called $P^{op}$-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 $k[x_p, p \in P]$ 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 {\it maximal} minors and whose initial ideals are letterplace ideals of prinicpal poset ideals. 29 pages |
| Databáze: | OpenAIRE |
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