Antimatroid
![Three views of an antimatroid: an inclusion ordering on its family of feasible sets, a formal language, and the corresponding path poset.](/Images/godic/202412/21/Antimatroid.svg3532.png")
![A shelling sequence of a planar point set. The line segments show edges of the convex hulls after some of the points have been removed.](/Images/godic/202412/21/Convex_shelling.svg3532.png")
In mathematics, an antimatroid is a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remains available until it is included. Antimatroids are commonly axiomatized in two equivalent ways, either as a set system modeling the possible states of such a process, or as a formal language modeling the different sequences in which elements may be included. Dilworth (1940) was the first to study antimatroids, using yet another axiomatization based on lattice theory, and they have been frequently rediscovered in other contexts; see Korte et al. (1991) for a comprehensive survey of antimatroid theory with many additional references.