Simplicial orders and Betti numbers of chordal hypergraphs

In this paper, we consider chordal clutters as it is defined in [7] and [1] via simplicial orders. The main importance of the chordal clutters in this sense is that their circuit ideal has a linear resolution, independent of the characteristic of the base field. Associated with any simplicial order is a sequence of integers which we call the -sequence of the chordal clutter. All possible -sequences are characterized. By the -sequence of a chordal clutter we determine other numerical invariants of the circuit ideal, such as the h-vector and the Betti numbers. We also show that any Betti sequence of an ideal with linear resolution appears as the Betti sequence of the circuit ideal of such a chordal clutter.