nLab decorated permutation

Definition

A decorated permutation of $[n]$ is a pair $(\pi, col)$, where $\pi \colon [n]\to[n]$ is a permutation, and $col$ is a function from fixed points of $\pi$ to the set $\{-1,1\}$.

Properties

Decorated permutations are in bijection with Grassmann necklaces.

Literature

Introduced in:

• Alexander Postnikov: Total positivity, Grassmannians, and networks [arXiv:math/0609764]

category: combinatorics