Resolutions of letterplace ideals of posets

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.