Associahedron - Revision history

Karl Jones: /* See also */

2016-08-24T18:37:32Z

‎See also

Karl Jones at 01:04, 14 May 2016

2016-05-14T01:04:10Z

Karl Jones: Created page with "In mathematics, an '''associahedron''' Kn is an (n − 2)-dimensional convex polytope in which each vertex corresponds to a way of correctly inserting opening and..."

2016-05-14T01:02:05Z

Created page with "In mathematics, an '''associahedron''' Kn is an (n − 2)-dimensional convex polytope in which each vertex corresponds to a way of correctly inserting opening and..."

New page

In [[mathematics]], an '''associahedron''' Kn is an (n − 2)-dimensional convex [[polytope]] in which each [[vertex]] corresponds to a way of correctly inserting opening and closing parentheses in a word of n letters and the edges correspond to single application of the [[associativity rule]].

== Description ==

Equivalently, the vertices of an associahedron correspond to the triangulations of a regular polygon with n + 1 sides and the edges correspond to edge flips in which a single diagonal is removed from a triangulation and replaced by a different diagonal.

Associahedra are also called ''Stasheff polytopes'' after the work of [[Jim Stasheff]], who rediscovered them in the early 1960s after earlier work on them by [[Dov Tamari]].

== See also ==

* [[Cyclohedron]], a polytope whose definition allows parentheses to wrap around in cyclic order.
* [[Permutohedron]], a polytope defined from commutativity in a similar way to the definition of the associahedron from associativity.
* [[Tamari lattice]], a lattice whose graph is the skeleton of the associahedron.

== External links ==

* [https://en.wikipedia.org/wiki/Associahedron Associahedron] @ Wikipedia

[[Category:Mathematics]]

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 * [[Associative property]]
 * [[Cyclohedron]], a polytope whose definition allows parentheses to wrap around in cyclic order.
 * [[Permutohedron]], a polytope defined from commutativity in a similar way to the definition of the associahedron from associativity.
 * [[Polytope]]

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-In [[mathematics]], an '''associahedron''' Kn is an (n − 2)-dimensional convex [[polytope]] in which each [[vertex]] corresponds to a way of correctly inserting opening and closing parentheses in a word of n letters and the edges correspond to single application of the [[associativity rule]].
+In [[mathematics]], an '''associahedron''' Kn is an (n − 2)-dimensional convex [[polytope]] in which each [[vertex]] corresponds to a way of correctly inserting opening and closing parentheses in a word of n letters and the edges correspond to single application of the [[Associative property|associativity rule]].
 == Description ==
@@ Line 9: / Line 9: @@
 == See also ==
 * [[Cyclohedron]], a polytope whose definition allows parentheses to wrap around in cyclic order.
 * [[Permutohedron]], a polytope defined from commutativity in a similar way to the definition of the associahedron from associativity.
 * [[Tamari lattice]], a lattice whose graph is the skeleton of the associahedron.