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A $k$factorization of the complete $t$uniform hypergraph $K^{(t)}_{v}$ is an $H$decomposition of $K^{(t)}_{v}$ where $H$ is a $k$regular spanning subhypergraph of $K^{(t)}_{v}$. We use nauty to generate the 2regular and 3regular spanning subhypergraphs of $K^{(3)}_v$ for $v\leq 9$ and investigate which of these subhypergraphs factorize $K^{(3)}_v$ or $K^{(3)}_vI$, where $I$ is a 1factor. We settle this question for all but two of these subhypergraphs.

Abstract The Electron Loss and Fields Investigation with a SpatioTemporal AmbiguityResolving option (ELFINSTAR, or heretoforth simply: ELFIN) mission comprises two identical 3Unit (3U) CubeSats on a polar (∼93 ∘ inclination), nearly circular, lowEarth (∼450 km altitude) orbit. Launched on September 15, 2018, ELFIN is expected to have a >2.5 year lifetime. Its primary science objective is to resolve the mechanism of stormtime relativistic electron precipitation, for which electromagnetic ion cyclotron (EMIC) waves are a prime candidate. From its ionospheric vantage point, ELFIN uses its unique pitchangleresolving capability to determine whether measured relativistic electron pitchangle and energy spectra within the loss cone bear the characteristic signatures of scattering by EMIC waves or whether such scattering may be due to other processes. Pairing identical ELFIN satellites with slowlyvariable alongtrack separation allows disambiguation of spatial and temporal evolution of the precipitation over minutestotensofminutes timescales, faster than the orbit period of a single lowaltitude satellite (T orbit ∼ 90 min). Each satellite carries an energetic particle detector for electrons (EPDE) that measures 50 keV to 5 MeV electrons with $\Delta $ Δ E/E < 40% and a fluxgate magnetometer (FGM) on a ∼72 cm boom that measures magnetic field waves (e.g., EMIC waves) in the range from DC tomore »