Enumeration of interval graphs and d-representable complexes

Abstract For each fixed d ≥ 1, we obtain asymptotic estimates for the number of d -representable simplicial complexes on n vertices as a function of n . The case d = 1 corresponds to counting interval graphs, and we obtain new results in this well-studied case as well. Our results imply that the d -representable complexes comprise a vanishingly small fraction of d -collapsible complexes.