Link invariants derived from multiplexing of crossings (Q1748451)

In this paper, the authors define an operation on the crossing set of a knot/link diagram called multiplexing. Let \(D\) be an \(n\)-component virtual link and \((m_1,\dots,m_n)\) be an ordered set of integers. Multiplexing of a (classical) crossing in relation with \(m_j\) whose overpass belongs to the \(j\)th component of \(D\), is to replace that crossing with virtual crossings and \(|m_j|\) classical crossings flanked around those virtual crossings. Let \(D(m_1,\dots,m_n)\) denote the virtual knot/link diagram obtained by multiplexing all classical crossings of \(D\) associated with \((m_1,\dots,m_n)\). The authors mainly prove that: 1. If \(D_1\) and \(D_2\) are two \(n\)-component welded isotopic virtual links then \(D_1(m_1,\dots,m_n)\) and \(D_2(m_1,\dots,m_n)\) are welded isotopic. 2. Let \(m\) be an integer greater or equal to 2, and \(D_1\) and \(D_2\) be two classical knot diagrams. Then \(D_1\) is equivalent to \(D_2\) or \(D_2^*\) (mirror of \(D_2\)) if and only if \(D_1(m)\) is welded isotopic to \(D_2(m)\).