# Permutation Lattice

Permutation Lattice

This Demonstration shows the lattice formed by sets of permutations ordered by inversions. Arrows in the lattice connect two permutations when one can be transformed to the other by inverting an adjacent pair of elements. The number of permutations at the level , , is the coefficient of in the expansion of , and the sum of those coefficients is .

k

k=1,…,n

x

k

∏∑x

n-1

j=1

j

i=0

i

n !