3 papers
math.CO2026
Generalizing OOOOOOB
Alon Danai, Paul Ellis, Thotsaporn Aek Thanatipanonda
We present three versions of the classic two-pile game \textsc{one-or-one-or-one-of-both} generalized to the multi-pile context. In each case, we explore the resulting $\mathcal{P}…
math.CO2026
Two Dimensional Subtraction -- Transfer Games
Alon Danai, Paul Ellis, Thotsaporn Aek Thanatipanonda
We generalize the results and conjectures of Tamás Lengyel, showing that the \textsc{nim}-values of a large class of two-dimensional subtraction-transfer games are periodic. These…
math.CO2026
Grid designs
Alon Danai, Joshua Kou, Andy Latto +2
We define a grid graph as a Cartesian product of path-graphs or cycle-graphs as shown in Figure 1, and we ask, when can the edge set of a complete graph be expresse…