Milnor invariants of sorting networks (Q2163425)

The authors investigate Milnor invariants of various braids arising from the signed sorting networks. By taking a given signed sorting network they relate their set to the set of sorting braids. Consider two sorting networks \(S\) and \(T\), the word \(ST\) corresponds to a closed loop on the permutahedron, so that if one assigns signatures to each crossing in the wiring diagram for \(ST,\) one gets a pure braid on \(n\) elements. It is then possible to study the Milnor invariants of these braids. The authors proceed to discuss the asymptotic invariants of two interesting special cases of sorting braids.