Letterplace and co-letterplace ideals of posets

Abstract

To a natural number $n$, a finite partially ordered set $P$ and a poset ideal $\mathcal{J}$ in the poset $Hom(P,[n])$ of isotonian maps from $P$ to the chain on $n$ elements, we associate two monomial ideals, the letterplace ideal $L(n,P;\mathcal{J})$ and the co-letterplace ideal $L(P,n;\mathcal{J})$. These ideals give a unified understanding of a number of ideals studied in monomial ideal theory in recent years. By cutting down these ideals by regular sequences of variable differences we obtain: multichain ideals and generalized Hibi type ideals, initial ideals of determinantal ideals, strongly stable ideals, $d$-partite $d$-uniform ideals, Ferrers ideals, edge ideals of cointerval $d$-hypergraphs, and uniform face ideals.

24 pages, updated introduction and references, and some minor improvements

References in corpus (4)

• Resolutions of letterplace ideals of posets
• The many polarizations of powers of maximal ideals
• Alexander duality for monomial ideals associated with isotone maps between posets
• The face ideal of a simplicial complex

Cited by in corpus (8)

• Resolutions of letterplace ideals of posets
• Algebraically rigid simplicial complexes and graphs
• The ideal of maximal flags of a poset
• Alexander duality for the alternative polarizations of strongly stable ideals
• Algebraic properties of ideals of poset homomorphisms
• On the relations of isotonian algebras
• Bi-Cohen-Macaulay graphs
• Cotangent cohomology of quadratic monomial ideals