3 papers
math.CO2026
A Ring structure on the Class of Combinatorial Games
Harry Altman, Paolo Lipparini
J. Conway defined useful operations on the Class of combinatorial games and also introduced a notion of equivalence between games. Conway showed that, under his equivalence, games…
math.CO2025
Infinite sums of combinatorial games (Dadaist games)
Paolo Lipparini
We propose an interpretation of the infinite sum of combinatorial games. In such an interpretation, plays involve infinite runs, but without loops. The notion of a run is quite nat…
math.LO2025
Monotone infinitary operations on ordinals (extended version)
Paolo Lipparini
We define and study an -ary operation on the class of the ordinals, which is strictly monotone in many significant cases (by an elementary argument, there is no fully strictly…