Tootfinder

My new puzzle is revisiting an old puzzle - just before they collapsed, I very nearly had #MyCroft in a useful form, but then it all fell apart and was feared lost.
But now there's an active fork: #OVOS won't see my HP laptop microphone (UbuntuStudio audio is pipewire, so that could be an issue, but it should emulate ALSA or pulseaudio!)

Matchings in multipartite hypergraphs
Candida Bowtell, Richard Mycroft
https://arxiv.org/abs/2403.05219 https://arxiv.org/pdf/2403.05…

Matchings in multipartite hypergraphs
A folklore result on matchings in graphs states that if $G$ is a bipartite graph whose vertex classes $A$ and $B$ each have size $n$, with $\mathrm{deg}(u) \geq a$ for every $u \in A$ and $\mathrm{deg}(v) \geq b$ for every $v \in B$, then $G$ admits a matching of size $\min\{n, a+b\}$. In this paper we establish the analogous result for large $k$-partite $k$-uniform hypergraphs, answering a question of Han, Zang and Zhao, who previously demonstrated that this result holds under the additional c…