Geodesic
A \(\beta\) invariant for greedoids and antimatroids
The electronic journal of combinatorics, Tome 4 (1997) no. 1
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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 $\beta (G)=1-b(G)$.
DOI : 10.37236/1298
Classification : 05B35
Mots-clés : matroids, greedoids, antimatroids, chordal graphs 
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     author = {Gary Gordon},
     title = {A \(\beta\) invariant for greedoids and antimatroids},
     journal = {The electronic journal of combinatorics},
     year = {1997},
     volume = {4},
     number = {1},
     doi = {10.37236/1298},
     zbl = {0885.05049},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1298/}
}
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Gary Gordon. A \(\beta\) invariant for greedoids and antimatroids. The electronic journal of combinatorics, Tome 4 (1997) no. 1. doi: 10.37236/1298

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