A recursive process related to a partizan variation of wythoff

• Autor(a) principal: Carvalho, Alda
• Data de Publicação: 2012
• Outros Autores: Santos, Carlos P., Dias, Cátia Lente, Coelho, Francisco, Neto, João Pedro, Vinagre, Sandra
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10174/5240
• topic: Combinatorial Game Theory; Partizan Games

Wythoff queens is a classical combinatorial game related to very interesting mathematical results. An amazing one is the fact that the P-positions are given by $(\lfloor \phi n, \phi^2 n \rfloor)$ and $(\lfloor \phi^2 n, \phi n \rfloor)$ where $\phi = \frac{1 + \sqrt{5}}{2}$. In this paper, we analyze a different version where one player (Left) plays with a chess bishop and the other (Right) plays with a chess knight. The new game (call it chessfights) lacks a Beatty sequence structure in the P-positions as in wythoff queens. However, it is possible to formulate and prove some general results of a general recursive law which is a particular case of a partizan subtraction game.