On a combination of the cyclic Nimhoff and subtraction games

Abstract

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