Geodesic
Matroid shellability, $\beta$-systems, and affine hyperplane arrangements
Journal of Algebraic Combinatorics, Tome 1 (1992) no. 3, pp. 283-300.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The broken-circuit complex is fundamental to the shellability and homology of matroids, geometric lattices, and linear hyperplane arrangements. This paper introduces and studies the [ `$( BC)] ( M) \overline $BC (M) , and the basic cycles are explicitly constructed. Similarly, an EL-shelling for the geometric semilattice associated with $M$ is produced,_and it is shown that the [ `$( BC)] ( M) \overline $BC (M) The intersection poset of any (real or complex) afflnehyperplane arrangement $Agr$ is a geometric semilattice. Thus the construction yields a set of basic cycles, indexed by $betanbc( M)$, for the union $xcupAgr$ of such an arrangement.
Keywords: matroid, $beta$-invariant, broken-circuit complex, shellability, affine hyperplane arrangement 
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     author = {Ziegler, G\"unter M.},
     title = {Matroid shellability, $\beta$-systems, and affine hyperplane arrangements},
     journal = {Journal of Algebraic Combinatorics},
     pages = {283--300},
     publisher = {mathdoc},
     volume = {1},
     number = {3},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1992__1_3_a0/}
}
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Ziegler, Günter M. Matroid shellability, $\beta$-systems, and affine hyperplane arrangements. Journal of Algebraic Combinatorics, Tome 1 (1992) no. 3, pp. 283-300. http://geodesic.mathdoc.fr/item/JAC_1992__1_3_a0/