Year: 2026
Type: preprint
Abstract: Suppose that $n=2m$, $k=2t$ and $n > 10 k^7$. We show that if a family $\mathcal F$ of $k$-subsets of an $n$-set has only even pairwise intersections then $|\mathcal F| \leq \binom{m}{t}$. Moreover, every extremal family has an atomic structure. This result was previously proved by Frankl and Tokushige for $n > n_{FT}(k)$, where $n_{FT}(k)$ is at least exponential. The main technique is Delsarte linear programming.
Source: arXiv (Cornell University)
Authors: Cherkashin, Danila, Prozorov, Pavel
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7201884273
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