The Erdös–Szekeres tableau

of a permutation

is the sequence of points

where

(respectively

) is the length of the longest increasing (respectively decreasing) subsequence ending at

. Since different permutations can have the same Erdös–Szekeres tableau (EST) (e.g.

and

both have the same "N-shaped" EST), there is an equivalence relation on permutations

. The poset is defined by taking the intersection over all orderings induced by elements of

. Informally, the poset records those relations that can be recovered from the EST. The lattice is defined on

, where

is in the covering relation if

and

differ by an adjacent transposition (which can be viewed as an edge label) and

precedes

lexicographically.