A knot diagram has an associated looped interlacement graph, obtained from the intersection graph of the Gauss diagram by attaching loops to the vertices that correspond to negative crossings. This… (More)

Let S be a double occurrence word, and let M S be the word's interlacement matrix, regarded as a matrix over GF (2). Gauss addressed the question of which double occurrence words are realizable by… (More)

A knot diagram has an associated looped interlacement graph, obtained from the intersection graph of the Gauss diagram by attaching loops to the vertices that correspond to negative crossings. This… (More)

We discuss the production of ortho-projection graphs from alternating knot diagrams, and introduce a more general construction of such graphs from “splittings” of closed, non-orientable surfaces. As… (More)