1 citations · 1 across the 11 of their papers we have counts for
12 papers
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…
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},\…
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…
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 under…
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…
A complete solution for the partisan chocolate game
Tomoaki Abuku, Hikaru Manabe, Richard J. Nowakowski +2
The class of Poset Take-Away games includes many interesting and difficult games. Playing on an -dimensional positive quadrant (the origin being the bottom of the poset) gives r…
Some extensions of Delete Nim
Tomoaki Abuku, Ko Sakai, Masato Shinoda +1
Nim is a well-known combinatorial game with several variants, e.g., Delete Nim and Variant Delete Nim. In Variant Delete Nim, the player deletes one of the two heaps of stones and…
Multiple Hook Removing Game Whose Starting Position is a Rectangular Young Diagram with the Unimodal Numbering
Tomoaki Abuku, Masato Tada
We introduce a new impartial game, named Multiple Hook Removing Game (MHRG for short). We also determine the -values of some game positions (including the starting pos…
Delete Nim
Koki Suetsugu, Tomoaki Abuku
In this paper, we study an impartial game called Delete Nim. In this game, there are two heaps of stones. The player chooses one of the heaps and delete the other heap. Next, she t…
On a Combination of the Cyclic Nimhoff and Subtraction Games
Tomoaki Abuku, Masanori Fukui, Ko Sakai +1
In this paper, we study a combination (called the generalized cyclic Nimhoff) of the cyclic Nimhoff and subtraction games. We give the -value of the game when all the…
Ryuo Nim: A Variant of the classical game of Wythoff Nim
Ryohei Miyadera, Yuki Tokuni, Yushi Nakaya +3
The authors introduce the impartial game of the generalized Ryūō Nim, a variant of the classical game of Wythoff Nim. In the latter game, two players take turns in moving a single…
Transfinite Version of Welter's Game
Tomoaki Abuku
We study the transfinite version of Welter's Game, a combinatorial game played on a belt divided into squares numbered with general ordinal. In particular, we give a straight-forwa…