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math.CO2025
Row Impartial Terminus
Eric Gottlieb, Dawood Khatana, Matjaž Krnc +2
We introduce Row Impartial Terminus (RIT), an impartial combinatorial game played on integer partitions. We show that any position in RIT can be uniquely decomposed into a core and…
math.CO2025
Nim on Integer Partitions and Hyperrectangles
Eric Gottlieb, Matjaž Krnc, Peter Muršič
We describe PNim and RNim, two variants of Nim in which piles of tokens are replaced with integer partitions or hyperrectangles. In PNim, the players choose one of the integer part…
math.CO2025
Impartial Chess on Integer Partitions
Eric Gottlieb, Matjaž Krnc, Peter Muršič
Berlekamp proposed a class of impartial combinatorial games based on the moves of chess pieces on rectangular boards. We generalize impartial chess games by playing them on Young d…