We introduce a graph polynomial that distinguishes tree structures to represent dependency
grammar and a measure based on the polynomial representation to quantify syntax …

This paper concerns the braid index of an alternating link. It is well known that the braid
index of any link equals the minimum number of Seifert circles among all link diagrams …

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 …

We discuss relations among various positivities of knots and links, such as strong
quasipositivity and quasipositivity. We give several pieces of supporting evidence for …

A long standing open conjecture states that if a link $\mathcal {K} $ is alternating, then its
ropelength $ L (\mathcal {K}) $ is at least of the order $ O (Cr (\mathcal {K})) $. A recent result …

We provide a combinatorial characterisation of positive diagrams satisfying the equality in
the Morton-Franks-Williams bound for the degrees of the HOMFLY-PT polynomial. This …

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 …

We discuss when homogeneous quasipositive links are positive. We show that a
homogeneous diagram of a quasipositive link whose number of Seifert circles is equal to the …

This paper introduces a novel graph polynomial approach for differentiating tree structures
in dependency grammar. Utilizing this polynomial representation, we develop a metric to …

Adapting the graph index to be used for braided surfaces, we gain realization results on
string numbers of Bennequin surfaces. In particular, all fibered alternating links and pure …