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math.CO2026
Short proofs in combinatorics and number theory
Boris Alexeev, Moe Putterman, Mehtaab Sawhney +2
We give a triplet of short proofs, each of which answers a question raised by ErdÅs. The first concerns the small prime factors of , the second concerns whether an a…
math.CO2024
The Penults of Tak: Adventures in impartial, normal-play, positional games
Boris Alexeev, Paul Ellis, Michael Richter +1
For normal play, impartial games, we define penults as those positions in which every option results in an immediate win for the other player. We explore the number of tokens in pe…