1 citations · 1 across the 11 of their papers we have counts for
Showing 2025Show all
3 papers · 1 filter
math.CO2025
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…
math.CO2025
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},\…
math.CO2025
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…