Measuring a knot's distance from alternating

Adam Lowrance (Vassar)

Abstract: A knot invariant d(K) measures a knot's distance from alternating if d(K) is a non-negative integer such that d(K)=0 if and only if K is alternating and such that d(K_1 #K_2)<= d(K_1)+d(K_2). We compare and contrast several such distance invariants, including dealternating number, alternation number, alternating genus, Turaev genus, and warping span.