arXiv subjects

Ko Sakai

Publications and source records attributed to Ko Sakai.

3 recordsLinked to original sources

arXiv2023

Some extensions of Delete Nim

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 splits the other heap on his/her turn. In this paper, we discuss generalized Variant Delete Nim, which generalizes the number of stone heaps to three or more, All-but-one-delete Nim, Half-delete Nim, No-more-than-half-delete Nim, and Single-delete Nim. We study the win-loss conditions for each of these games.

math.CO↗

arXiv2019

On a Combination of the Cyclic Nimhoff and Subtraction Games

In this paper, we study a combination (called the generalized cyclic Nimhoff) of the cyclic Nimhoff and subtraction games. We give the $\mathcal{G}$-value of the game when all the $\mathcal{G}$-value sequence of subtraction games have a common $h$-stair structure.

math.CO↗

arXiv2016

Construction of Gray maps for groups of order 16

In this paper we consider Type 1 Gray maps and Type 2 Gray maps for groups of order 16. First, we confirm that we can construct Type 1 Gray maps for all groups of order 16, and we actually construct them. Next, we confirm that we can construct Type 2 Gray maps for several groups of order 16, and we construct all such maps. Finally we reveal why the other groups do not admit Gray maps.

cs.IT↗