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Summary

Description
English: The Hasse diagram of a Tamari lattice.
Français : Le diagramme de Hasse d'un treillis de Tamari
Date
Source Own work
Author David Eppstein
Permission
(Reusing this file)
Public domain 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

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 5 choose 2 array, hexagonal.svg Ovals Parentheses
Vertices
(and
edges)
Tamari lattice, hexagons.svg Tamari lattice, trees.svg Tamari lattice, 2-subsets.svg Tamari lattice, ovals.svg Tamari lattice.svg
Faces Tamari lattice, trees, with face labels.svg Associahedron K5 faces, 2-subsets.svg Associahedron K5 faces, ovals.svg

File history

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Date/TimeThumbnailDimensionsUserComment
current15:46, 19 November 2013Thumbnail for version as of 15:46, 19 November 2013504 × 702 (7 KB)Watchduckadd missing bracket
02:14, 13 March 2010Thumbnail for version as of 02:14, 13 March 2010504 × 702 (4 KB)David EppsteinUpdate to commons-compatible fonts
06:30, 23 November 2008Thumbnail for version as of 06:30, 23 November 2008504 × 702 (4 KB)David Eppstein{{Information |Description={{en|1=The Hasse diagram of a Tamari lattice.}} |Source=Own work by uploader |Author=David Eppstein |Date=November 22, 2008 |Permission= |other_versions= }} <
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