3 papers
math.CO2026
Impartial Combinatorial Games and the Nuclear Escalation Ladder
Arnav Garg
We model Herman Kahn's escalation ladder as an impartial combinatorial game. Reindexing each rung by its distance to the nuclear threshold turns the ladder into a subtraction game,…
math.CO2026
Proof of Conjecture 19 of Ballantine, Beck, Merca, and Sagan on Elementary Symmetric Partitions
Arnav Garg
Ballantine, Beck, Merca, and Sagan conjectured four identities, collectively Conjecture 19, relating the image of the map pre_k on integer partitions to four OEIS sequences. We pro…
math.CO2026
A note on partitions in the image of pre
Arnav Garg
Devnani and Eyyunni recently studied the maps pre on integer partitions, which arise from applying elementary symmetric polynomials to the parts of a partition. They asked whet…