Resolutions of letterplace ideals of posets

Abstract

We investigate resolutions of letterplace ideals of posets. We develop topological results to compute their multigraded Betti numbers, and to give structural results on these Betti numbers. If the poset is a union of no more than $c$ chains, we show that the Betti numbers may be computed from simplicial complexes of no more than $c$ vertices. We also give a recursive procedure to compute the Betti diagrams when the Hasse diagram of $P$ has tree structure.

21 pages

References in corpus (3)

• Letterplace and co-letterplace ideals of posets
• Resolutions of letterplace ideals of posets
• Alexander duality for monomial ideals associated with isotone maps between posets

Cited by in corpus (3)

• Letterplace and co-letterplace ideals of posets
• Resolutions of letterplace ideals of posets
• Algebraic properties of ideals of poset homomorphisms