4 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…