Shellability of Oriented Matroids
نویسنده
چکیده
In Man82] A. Mandel proved that the maximal cells of an Oriented Matroid poset are B-shellable. Our result shows that the whole Oriented Matroid is shellable, too.
منابع مشابه
Matroid Shellability , β - Systems and Affine Hyperplane Arrangements
The broken circuit complex plays a fundamental role for the shellability and homology of matroids, geometric lattices and linear hyperplane arrangements. Here we introduce and study the β-system of a matroid, βnbc(M), whose cardinality is Crapo’s β-invariant. In studying the shellability and homology of base-pointed matroids, geometric semilattices and affine hyperplane arrangements, we find th...
متن کاملChordal and Sequentially Cohen-Macaulay Clutters
We extend the definition of chordal from graphs to clutters. The resulting family generalizes both chordal graphs and matroids, and obeys many of the same algebraic and geometric properties. Specifically, the independence complex of a chordal clutter is shellable, hence sequentially Cohen-Macaulay; and the circuit ideal of a certain complement to such a clutter has a linear resolution. Minimal ...
متن کاملOn the Topology of the Combinatorial Flag Varieties —From a New Point of View
We prove that the simplicial complex Ωn of chains of matroids (with respect to the ordering by the quotient relation) on n elements is shellable. This follows from a more general result on shellability of the simplicial complex of W -matroids for an arbitrary finite Coxeter group W . The paper generalises the well known results by Solomon-Tits and Björner on spherical buildings, and improves th...
متن کاملOriented Matroids Today
This dynamic survey offers an “entry point” for current research in oriented matroids. For this, it provides updates on the 1993 monograph “Oriented Matroids” by Björner, Las Vergnas, Sturmfels, White & Ziegler [73], in three parts: 1. a sketch of a few “Frontiers of Research” in oriented matroid theory, 2. an update of corrections, comments and progress as compared to [73], and 3. an extensive...
متن کاملThe flow lattice of oriented matroids
Recently Hochstättler and Nešetřil introduced the flow lattice of an oriented matroid as generalization of the lattice of all integer flows of a digraph or more general a regular matroid. This lattice is defined as the integer hull of the characteristic vectors of signed circuits. Here, we characterize the flow lattice of oriented matroids that are uniform or have rank 3 with a particular focus...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1990