5 papers
Combinatorial games and the golden ratio on digraphs
Tomoaki Abuku, Hiroki Inazu, Hiyu Inoue +4
We introduce a new combinatorial game called Triangle Game. In this game, a directed -cycle graph is given, and stones are placed on each vertex. The player chooses a directed e…
Various Diamond Properties in Combinatorial Game Theory
Keiichirou Kusakari, Tomoaki Abuku
We investigate conditions under which positions in combinatorial games admit simple values. We introduce a unified diamond framework, the -property ($A\in\{\mathbb{Z},\…
Cyclic impartial games with carry-on moves
Tomoaki Abuku, Alda Carvalho, Urban Larsson +3
In an impartial combinatorial game, both players have the same options in the game and all its subpositions. The classical Sprague-Grundy Theory was developed for short impartial g…
Relationship between misère NIM and two-player GOISHI HIROI
Tomoaki Abuku, Masanori Fukui, Shin-ichi Katayama +1
In combinatorial game theory, there are two famous winning conventions, normal play and misère play. Under normal play convention, the winner is the player who moves last and unde…
Enforce and selective operators of combinatorial games
Tomoaki Abuku, Shun-ichi Kimura, Hironori Kiya +4
We consider an {\em enforce operator} on impartial rulesets similar to the Muller Twist and the comply/constrain operator of Smith and St\u anic\u a, 2002. Applied to the rulesets…