# Tamari Lattice

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

There are multiple ways to parenthesize a sequence of factors two at a time. For instance, , , and can be grouped as either or ; the Catalan numbers count the number of ways this is possible for factors. The groupings form a partially ordered set, where one grouping covers another if the first can be transformed into the second by taking a subelement of the form and replacing it with . In these transformations, , , and can be a single factor or a product of factors. These partially ordered sets form a lattice called the Tamari lattice.

[more]
Contributed by: Robert Dickau (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

R. P. Stanley, *Enumerative Combinatorics**, Volume 2*, Cambridge: Cambridge University Press, 1999 pp. 234–235.

## Permanent Citation

"Tamari Lattice"

http://demonstrations.wolfram.com/TamariLattice/

Wolfram Demonstrations Project

Published: March 7 2011