It is an open question whether there are Vassiliev invariants that can distinguish an oriented knot from its inverse, i.e., the knot with the opposite orientation. In this article, an example is given for a first order Vassiliev invariant that takes different values on a virtual knot and its inverse. The Vassiliev invariant is derived from the Conway polynomial for virtual knots. Furthermore, i...

The authors reanalyzed assessment center (AC) multitrait-multimethod (MTMM) matrices containing correlations among postexercise dimension ratings (PEDRs) reported by F. Lievens and J. M. Conway (2001). Unlike F. Lievens and J. M. Conway, who used a correlated dimension-correlated uniqueness model, we used a different set of confirmatory-factor-analysis-based models (1-dimension-correlated Exerc...

Suppose a link K in a 3-manifold M is in bridge position with respect to two different bridge surfaces P and Q, both of which are c-weakly incompressible in the complement of K. Then either • P and Q can be properly isotoped to intersect in a nonempty collection of curves that are essential on both surfaces, or • K is a Conway product with respect to an incompressible Conway sphere that natural...

The Leech lattice A is a very dense packing of spheres in 24-dimensional Euclidean space, discovered by Leech (1967). Its automorphism group was determined by Conway (1969), and its usefulness as a source of codes for the Gaussian channel was studied by Blake (1971). The present note contains some comments on and corrections to the latter paper. Both Leech (1967) and Conway (1969) use essential...

Combinatorial Game Theory is a fascinating and rich theory, based on a simple and intuitive recursive definition of games, which yields a very rich algebraic structure: games can be added and subtracted in a very natural way, forming an abelian GROUP (§ 2). There is a distinguished subGROUP of games called numbers which can also be multiplied and which form a FIELD (§ 3): this field contains bo...

In this paper we study diagonal quadratic forms which are universal when restricted to almost prime inputs, establishing finiteness theorems akin the Conway–Schneeberger 15 theorem.

We consider Conway polynomials of two-bridge links as Euler continuant polynomials. As a consequence, we obtain simple proofs of the classical theorems of Murasugi and Hartley on Alexander polynomials. We give a modulo 2 congruence for links, which implies the classical modulo 2 Murasugi congruence for knots. We also give sharp bounds for the coefficients of the Conway and Alexander polynomials...

The axioms of iteration theories, or iteration categories, capture the equational properties of fixed point operations in several computationally significant categories. Iteration categories may be axiomatized by the Conway identities and identities associated with finite automata. We show that the Conway identities and the identities associated with the members of a subclass Q of finite automa...

Pairs of genus 2 mutant knots can have different Homfly polynomials, for example some 3-string satellites of Conway mutant pairs. We give examples which have different Kauffman 2-variable polynomials, answering a question raised by Dunfield et al in their study of genus 2 mutants. While pairs of genus 2 mutant knots have the same Jones polynomial, given from the Homfly polynomial by setting v =...