File:Tamari lattice, ovals.svg

Summary[edit]

DescriptionTamari lattice, ovals.svg	The associahedron of order 4 (or K5), the Hasse diagram of the Tamari lattice of order 4 Like File:Tamari lattice.svg, but with the parentheses closed to ovals.
Source	Own work
Author	Watchduck You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
Permission (Reusing this file)	Public domainPublic domainfalsefalse I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Overview[edit]

The associahedron K5 has C₄ = 14 vertices, 21 edges and T₄−1 = 9 faces.
Each one of the faces corresponds to a 2-subset of {1,2,3,4,5} except {1,5}. Faces whose 2-subsets overlap do not touch.
(Overlap would mean that an element in one set is between the elements of the other, like with {1,3} and {2,4}.)
An edge or vertex corresponds to a set that contains the 2-subsets of the faces that meet in this edge or vertex.

	Triangulated hexagons	Binary trees	Sets of 2-subsets	Ovals	Parentheses
Vertices (and edges)
Faces