Transposition game

Elise Janvresse (1) , Steve Kalikow (2) , Thierry de La Rue (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 Department of Mathematics

We introduce a two-player game, in which each player extends a given sequence by picking a free element in a domain D of the real line. The aim of the players is to control the parity of the number of transpositions necessary to put the final sequence in order. We will see that the winner can be the last player, the second last player, the first player, the second player, the person who wants the parity to end up even or the person who wants the parity to end up odd. A special case of the game can be reduced to a game with nontrivial winning strategy, but describable in so simple a way that children can understand it and enjoy playing it.

Mots clés: 2-person game; parity of a permutation

Domaines: Combinatoire [math.CO]

Elise Janvresse, Steve Kalikow, Thierry de La Rue. Transposition game. 2009. ⟨hal-00372006v2⟩