In this paper, we enumerate the number of oriented rational knots and the number of
oriented rational links with any given crossing number and minimum genus. This allows us …

We prove a simple necessary and sufficient condition for a two-bridge knot K (p, q) to be
quasipositive, based on the continued fraction expansion of p/q. As an application, coupled …

The braid indices of most links remain unknown as there is no known universal method for
determining the braid index of an arbitrary knot. This is also the case for alternating knots …

In this paper, we are interested in BB knots, namely knots and links whose bridge index and
braid index are equal. Supported by observations from experiments, it is conjectured that BB …

The determination of the braid index of an oriented link is generally a hard problem. In the
case of alternating links, some significant progresses have been made in recent years which …

In this paper, we tabulate the set of alternating pretzel links. Specifically, for any given
crossing number $ c $, we derive a closed formula that would allow us to compute $\mathcal …

A rational link may be represented by any of the (infinitely) many link diagrams
corresponding to various continued fraction expansions of the same rational number. The …

It is known that the writhe calculated from any reduced alternating link diagram of the same
(alternating) link has the same value. That is, it is a link invariant if we restrict ourselves to …

An effectively verifiable condition for quasipositivity of links is given. In particular, it is proven
that if a quasipositive link can be represented by an alternating diagram satisfying the …

A spiral knot or link diagram (introduced in [C. Adams, R. Hudson, R. Morrison, W. George,
L. Starkston, S. Taylor and O. Turanova, The spiral index of knots, Math. Proc. Cambridge …