In the geometry of
convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n. Most texts. use the term "polytope" for a bounded convex polytope, and the wo ...
s, a distributive polytope is a convex polytope for which coordinatewise minima and maxima of pairs of points remain within the polytope. For example, this property is true of the
unit cube, so the unit cube is a distributive polytope. It is called a distributive polytope because the coordinatewise minimum and coordinatewise maximum operations form the meet and join operations of a continuous
distributive lattice on the points of the polytope.
Every face of a distributive polytope is itself a distributive polytope. The distributive polytopes all of whose vertex coordinates are 0 or 1 are exactly the
order polytopes.
See also
*
Stable matching polytope In mathematics, economics, and computer science, the stable matching polytope or stable marriage polytope is a convex polytope derived from the solutions to an instance of the stable matching problem.
Description
The stable matching polytope is the ...
, a convex polytope that defines a distributive lattice on its points in a different way
References
{{reflist, refs=
[{{citation
, last1 = Felsner , first1 = Stefan
, last2 = Knauer , first2 = Kolja
, doi = 10.1016/j.ejc.2010.07.011
, issue = 1
, journal = ]European Journal of Combinatorics
European, or Europeans, or Europeneans, may refer to:
In general
* ''European'', an adjective referring to something of, from, or related to Europe
** Ethnic groups in Europe
** Demographics of Europe
** European cuisine, the cuisines of Europe ...
, mr = 2727459
, pages = 45–59
, title = Distributive lattices, polyhedra, and generalized flows
, volume = 32
, year = 2011, doi-access = free
.
Order theory
Polytopes