# Permutation Grid Classes

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A grid class of permutations is defined by a 0/1/-1 matrix, which specifies the shape of plots of the permutations in the class. Each cell in the matrix corresponds to a rectangle in a "gridding" of a permutation. If the cell in the matrix contains 1, any points in the rectangle must form an increasing sequence; if the cell contains -1, any points in the rectangle must form a decreasing sequence; if the cell is 0, the rectangle must be empty. An empty sequence is both increasing and decreasing. A permutation in a grid class may have multiple possible griddings.

Contributed by: David Bevan (June 2012)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Click in either the numeric or graphical representation of the matrix to change the cell values.

Permutation grid classes are defined in [1].

Reference

[1] S. Huczynska and V. Vatter, "Grid Classes and the Fibonacci Dichotomy for Restricted Permutations," *Electronic Journal of Combinatorics*, 13(R54), 2006 pp. 1–14.

## Permanent Citation

"Permutation Grid Classes"

http://demonstrations.wolfram.com/PermutationGridClasses/

Wolfram Demonstrations Project

Published: June 3 2012