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5 votes

Finite pair-splitting family of $\mathbb{N}$

$\newcommand\F{\mathfrak F}\newcommand\P{\mathfrak P}\newcommand\N{\mathbb N}\newcommand\om{\omega}$No. Let $\P$ be the partition of $\N$ generated by $\F$. Detail: If $\F=\{S_1,\dots,S_n\}$, then the ...
Iosif Pinelis's user avatar
4 votes

$\aleph_0$-uniform non-bipartite linear hypergraph

Every $\aleph_0$-uniform linear hypergraph is bipartite. More generally: Theorem. If $H=(V,E)$ is an $\aleph_0$-uniform hypergraph, and if there is a number $n\lt\aleph_0$ such that $|\{e\in E:S\...
bof's user avatar
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