A \(\beta\) invariant for greedoids and antimatroids (Q1378502)

Summary: We extend Crapo's \(\beta \) invariant from matroids to greedoids, concentrating especially on antimatroids. Several familiar expansions for \(\beta (G)\) have greedoid analogs. We give combinatorial interpretations for \(\beta (G)\) for simplicial shelling antimatroids associated with chordal graphs. When \(G\) is this antimatroid and \(b(G)\) is the number of blocks of the chordal graph \(G\), we prove \(\beta (G)=1-b(G)\).