Tamari's diagram

Scans of Fig. 1 in Tamari's 1951 thesis MR 51833 can be found here:

Stasheff, Jim. How I ‘met’ Dov Tamari. Associahedra, Tamari lattices and related structures, 45-63. Progr. Math., 299, 2012. MR 3221533.

Scan of Tamari's diagram

Here is a TeX/TikZ presentation:

TeX version of Tamari's diagram

[high resolution image]

The following colored variant has reversed arrows and perspective. It illustrates the strong deformation retractions

4 → ℳ3 → ℳ2 → ℳ1

The embeddings

1 → ℳ2 → ℳ3 → ℳ4

are given by prepending "1" to the labels. The green/red/blue arrows indicate the homotopies. In terms of the cubical view, these retract the cuboid linearly to a side.

Colored TeX version of Tamari's diagram

[high resolution image]

Source code


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