BRAIDS AND ORDER-PRESERVING PARTIAL PERMUTATIONS
James East · Journal of Knot Theory and Its Ramifications · 2010
We initiate a new way to study presentations of the inverse braid monoid [Formula: see text]. Our method makes use of the monoid [Formula: see text] of all order-preserving partial permutations on an n-element chain. As an application we derive the Easdown–Lavers (2004) presentation of [Formula: see text], and we also obtain new presentations for the symmetric inverse monoid [Formula: see text] and the monoid [Formula: see text] of all order-preserving partial braids with at most n strings.