v 1 2 4 A pr 1 99 5 A Link Invariant from Quantum Dilogarithm
The link invariant, arising from the cyclic quantum dilogarithm via the particular R-matrix construction, is proved to coincide with the invariant of triangulated links in S introduced in [14]. The obtained invariant, like Alexander-Conway polynomial, vanishes on disjoint union of links. The R-matrix can be considered as the cyclic analog of the universal R-matrix associated with Uq(sl(2)) algebra.
An enumeration of knots and links, and some of their algebraic properties
Publisher Summary This chapter describes knots and links, and some of their algebraic properties. An edge-connected 4-valent planar map is called a polyhedron, and a polyhedron is basic if no region has just 2 vertices. The term region includes the infinite region, which is regarded in the same light as the others. Knot diagrams can be obtained from polyhedra by substituting tangles for their vertices, for instance, tangles 1 or −1 could always be substituted. A knot diagram K can be obtained by substituting algebraic tangles for the vertices of some nonbasic polyhedron P. There is a polyhedron Q with fewer vertices than P obtained by shrinking some 2-vertex region of P, and K can simply be obtained by substituting algebraic tangles for the vertices of Q. Any knot diagram can be obtained by substituting algebraic tangles for the vertices of some basic polyhedron P in fact P, and the manner of substitution is essentially unique.
The effect of family size on parents' labor supply and occupational prestige: Evidence from Taiwan and Mainland China
Abstract This paper studies the effect of family size on parents' labor supply and occupational prestige, using the censuses of both Taiwan and Mainland China. We rely on the exogenous increase in child quantity that results from having twins at the first birth. Our results indicate that an increase in family size has negative effects on the labor supply of mothers, but not of fathers, in both Taiwan and Mainland China. In addition, we find that in Taiwan fathers tend to switch to occupations with lower prestige scores in response to an increase in family size. However, the negative effect of family size on occupational prestige is not observed in Mainland China, where the occupational mobility is low.