Nous appliquons le concept de séquences tressage aux polynômes skein et Conway, mais aussi à quelques invariants géométriques des entrelacs positifs. On donne estimations pour l’indice tresses legendriens, en utilisant degré propriétés croissance coefficients du polynôme Conway. énumérons asymptotiquement une constante près les alternants (et autres) genre donné par leur indice tresses.

Using coalgebraic methods, we extend Conway’s original theory of games to include infinite games (hypergames). We take the view that a play which goes on forever is a draw, and hence rather than focussing on winning strategies, we focus on non-losing strategies. Infinite games are a fruitful metaphor for non-terminating processes, Conway’s sum of games being similar to shuffling. Hypergames hav...

We conjecture that for the Conway polynomial C(z) of an amphicheiral knot, the product C(z)C(iz)C(z 2) must be a square inside the ring of polynomials with Z 4 coefficients. This conjecture has two ancestors. One is a theorem of Kawauchi and Hartley, which says that the Conway polynomial of a strongly amphicheiral knot must decompose as φ(z)φ(−z). This implies our main conjecture, at least for ...

A Conway semiring is a semiring S equipped with a unary operation * : S → S, always called 'star', satisfying the sum star and product star identities. It is known that these identities imply a Kleene type theorem. Some computationally important semirings, such as N or N rat Σ * of rational power series of words on Σ with coefficients in N, cannot have a total star operation satisfying the Conw...