Rknots (version 1.3.1)

skeinIterator: Iterate the skein relation to build a skein tree of a polygonal link

Description

This function is required for the computation of the skein tree of a polygonal link. The tree is built by iterating the skein relation and geometrically constructing the $L_0$ and $L_{sw}$ configuration (of a Conway skein triple).

Usage

skeinIterator(points3D, ends, M = c())

Arguments

points3D

an $N$ x 3 matrix of the $x$, $y$, $z$ coordinates of a polygonal link

ends

a vector of positive integers defining the separators of the polygonal link

M

the intersection matrix of the polygonal link

Value

leaves

a list containing the binary indices of the tree leaves

tree

a list containing the skein tree. Each slot contains the slots points3D, ends, signs and M, which are respectively the coordinates, separators of the current configuration, the skein signs of the ancestors (inner vertices) and the intersection matrix of the current configuration.

References

Freyd P, Yetter D, Hoste J, Lickorish WBR, Millett K, et al. (1985) A new polynomial invariant of knots and links. Bull Amer Math Soc (NS) 12: 239-246. Kauffman, L. Knots and Physics. Teaneck, NJ: World Scientific, p. 19, 1991. Comoglio F. and Rinaldi M. A Topological Framework for the Computation of the HOMFLY Polynomial and Its Application to Proteins (2011) PLoS ONE 6(4): e18693, doi:10.1371/journal.pone.0018693 ArXiv:1104.3405

See Also

HOMFLYpolynomial,

Examples

	protein <- makeExampleProtein()
	protein <- AlexanderBriggs(protein$A)

	## Compute the skein tree
	tree <- skeinIterator(protein$points3D, protein$ends)
	str(tree)