A $\beta$ Invariant for Greedoids and Antimatroids
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 $\beta (G)=1-b(G)$.
1993 ◽
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2002 ◽
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2009 ◽
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pp. 710-735
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