arXiv subjects

Moe Putterman

Publications and source records attributed to Moe Putterman.

3 recordsLinked to original sources

arXiv2026

Short proofs in combinatorics, probability and number theory II

We give a quintet of proofs resulting from questions posed by Erd\H{o}s. These questions concern ordinary lines in planar point sets, sequences with uniformly small exponential sums, $K_4$-free $4$-critical graphs with few chords in any cycle, a counterexample to a "fewnomial" version of the Erd\H{o}s--Tur\'{a}n discrepancy bound, and a finiteness theorem for integers $n$ such that $n-a k^2$ is prime for all $k\leq \sqrt{n/a}$ coprime to $n$ (for fixed $a\in\mathbb Z_+$). Each proof is due to an internal model at OpenAI.

math.CO↗

arXiv2026

Short proofs in combinatorics and number theory

We give a triplet of short proofs, each of which answers a question raised by Erd\H{o}s. The first concerns the small prime factors of $\binom{n}{k}$, the second concerns whether an additive basis $A$ can always be split into pieces $A_1$ and $A_2$ such that each of $A_i + A_i$ has bounded gaps, and the final concerns whether $\{\alpha p\}$ is "well-distributed" in the sense introduced by Hlawka and Petersen. In each case, the proof is due entirely to an internal model at OpenAI.

math.CO↗

arXiv2026

On infinite sets with no $3$ on a line

We give a construction of an infinite set of points $A$ in $\mathbb{R}^2$ such that any subset $P\subseteq A$ has a constant density subset $P'$ with no three points collinear and yet $A$ cannot be separated into finitely many subsets such that each subset has no three points collinear. This provides a new proof of a question of Erd\H{o}s, Ne\v{s}et\v{r}il, and R\"{o}dl. The construction was generated by an internal model at OpenAI.

math.CO↗