Abstract
We propose a definition of an oriented interval greedoid that simultaneously generalizes the notion of an oriented matroid and the construction on antimatroids introduced by L.J. Billera, S.K. Hsiao, and J.S. Provan in Enumeration in convex geometries and associated polytopal subdivisions of spheres (Discrete Comput. Geom. 39(1–3):123–137, 2008). As for oriented matroids, associated to each oriented interval greedoid is a spherical simplicial complex whose face enumeration depends only on the underlying interval greedoid.
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Saliola, F., Thomas, H. Oriented Interval Greedoids. Discrete Comput Geom 47, 64–105 (2012). https://doi.org/10.1007/s00454-011-9383-3
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DOI: https://doi.org/10.1007/s00454-011-9383-3