The Malicious Maitre D’ At a mathematics conference banquet, 48 male mathematicians, none of them knowledgeable about table etiquette, find themselves assigned to a big circular table. On the table, between each pair of settings, is a coffee cup containing a cloth napkin. As each person is seated (by the maitre d’), he takes a napkin from his left or right; if both napkins are present, he choos...

After defining reduced minimum braid word and criteria for a braid family representative , different braid family representatives are derived, and a correspondence between them and families of knots and links given in Conway notation is established.

For analyzing impartial games played in the misère rule, Yamasaki defined flatness of games, while Conway defined tameness. In this paper, we prove that these two concepts are equivalent.

1 Lecture 1: Codes and groups 2 1.1 Finite fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Matrix representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Conway polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Linear codes: generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1...

For each pair of coprime integers n > m ≥ 2 we construct pairs of non equivalent Conway irreducible hyperbolic knots with the same n-fold and m-fold cyclic branched covers. Mathematics Subject Classification (2000). Primary 57M25; Secondary 57M12, 57M50.