Sa'ul A. Blanco | Searcharxiv

arXiv2026

On balanced subfamilies of maximum complement-free families in the middle layer of the Boolean lattice

We study balanced subfamilies of the middle layer $\binom{[2n]}{n}$ of the Boolean lattice $2^{[2n]}$. A family $\mathcal{F}\subseteq\binom{[2n]}{n}$ is said to be balanced if every element in $[2n]$ appears in the same number of members of $\mathcal{F}$. A balanced subfamily of size 2 is exactly a complementary pair $\{A,[2n]\setminus A\}$, and therefore a family with no balanced subfamily of size $2$ has at most $\frac{1}{2}\binom{2n}{n}$ members. We show that for every $k\geq 1$ and all sufficiently large $n$, this maximum size is compatible with delaying the smallest size of a balanced subfamily until $2k+2$. More precisely, there exists a family $\mathcal{F}\subseteq\binom{[2n]}{n}$ of size $\frac{1}{2}\binom{2n}{n}$ with no balanced subfamilies of sizes $2,4,\ldots,2k$, but with a balanced subfamily of size $2k+2$. The proof is constructive and is obtained by lifting Taylor-Zwicker trade-robust magic-square games to self-dual selectors in the middle layer. This proves a recent conjecture of Moss and Pedersen.

math.CO↗

arXiv2025

GPT Editors, Not Authors: The Stylistic Footprint of LLMs in Academic Preprints

The proliferation of Large Language Models (LLMs) in late 2022 has impacted academic writing, threatening credibility, and causing institutional uncertainty. We seek to determine the degree to which LLMs are used to generate critical text as opposed to being used for editing, such as checking for grammar errors or inappropriate phrasing. In our study, we analyze arXiv papers for stylistic segmentation, which we measure by varying a PELT threshold against a Bayesian classifier trained on GPT-regenerated text. We find that LLM-attributed language is not predictive of stylistic segmentation, suggesting that when authors use LLMs, they do so uniformly, reducing the risk of hallucinations being introduced into academic preprints.

cs.CL↗