Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776996 | Discrete Mathematics | 2017 | 5 Pages |
Abstract
The notion of an abstract convex geometry, due to Edelman and Jamison (1984), offers an abstraction of the standard notion of convexity in a linear space. Kashiwabara et al. (2005) introduce the notion of a generalized convex shelling into RN and prove that a convex geometry may always be represented with such a shelling. We provide a new, shorter proof of their result using a representation theorem of Edelman and Jamison (1984) and deduce a different upper bound on the dimension of the shelling. Furthermore, in the spirit of Czédli (2014)[6], who shows that any 2-dimensional convex geometry may be embedded as circles in R2, we show that any convex geometry may be embedded as convex polygons in R2.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Michael Richter, Luke G. Rogers,