Add to ORKGABSTRACT. A quadruple crossing is a crossing in a projection of a knot or link that has four strands of the knot passing straight through it. A quadruple crossing projection is a projection such that all of the crossings are quadruple crossings. In a previous paper, it was proved that every knot and link has a quadruple crossing projection and hence, every knot has a minimal quadruple crossing number c4(K). In this paper, we investigate quadruple crossing number, and in particular, use the span of the bracket polynomial to determine quadruple crossing number for a variety of knots and links. 1
The problem of finding the crossing number of an arbitrary knot or link is a hard problem in general...
Abstract.We first show that the three-variable bracket polynomial is an invariant for reduced, alter...
AbstractMorton and Franks–Williams independently gave a lower bound for the braid index b(L) of a li...
ABSTRACT. A multi-crossing (or n-crossing) is a singular point in a projection at which n strands cr...
Abstract. A triple crossing is a crossing in a projection of a knot or link that has three strands o...
ABSTRACT. Introduced recently, an n-crossing is a singular point in a projection of a link at which ...
An n-crossing is a point in the projection of a knot where n strands cross so that each strand bisec...
Abstract. An increasing sequence of integers is said to be universal for knots if every knot has a r...
The aim of the present paper is to prove that the minimal number of virtual crossings for some famil...
AbstractThis paper provides bounds for the ropelength of a link in terms of the crossing numbers of ...
Klein links are a nonorientable counterpart to torus knots and links. It is shown that braids repres...
Abstract. Utilizing both twisting and writhing, we construct in-tegral tangles with few sticks, lead...
One of the most basic invariants of a knot K is its crossing number c(K), which is the minimal numbe...
For a certain infinite family of knots or links, we study the growth power ratios of their stick num...
A method is given for economically constructing any algebraic knot or link K. This construction, whi...
The problem of finding the crossing number of an arbitrary knot or link is a hard problem in general...
Abstract.We first show that the three-variable bracket polynomial is an invariant for reduced, alter...
AbstractMorton and Franks–Williams independently gave a lower bound for the braid index b(L) of a li...
ABSTRACT. A multi-crossing (or n-crossing) is a singular point in a projection at which n strands cr...
Abstract. A triple crossing is a crossing in a projection of a knot or link that has three strands o...
ABSTRACT. Introduced recently, an n-crossing is a singular point in a projection of a link at which ...
An n-crossing is a point in the projection of a knot where n strands cross so that each strand bisec...
Abstract. An increasing sequence of integers is said to be universal for knots if every knot has a r...
The aim of the present paper is to prove that the minimal number of virtual crossings for some famil...
AbstractThis paper provides bounds for the ropelength of a link in terms of the crossing numbers of ...
Klein links are a nonorientable counterpart to torus knots and links. It is shown that braids repres...
Abstract. Utilizing both twisting and writhing, we construct in-tegral tangles with few sticks, lead...
One of the most basic invariants of a knot K is its crossing number c(K), which is the minimal numbe...
For a certain infinite family of knots or links, we study the growth power ratios of their stick num...
A method is given for economically constructing any algebraic knot or link K. This construction, whi...
The problem of finding the crossing number of an arbitrary knot or link is a hard problem in general...
Abstract.We first show that the three-variable bracket polynomial is an invariant for reduced, alter...
AbstractMorton and Franks–Williams independently gave a lower bound for the braid index b(L) of a li...