permutahedral

English

Etymology

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Adjective

permutahedral (not comparable)

1. (mathematics) Relating to a permutahedron
   • 2016, Aruni Choudhary, Michael Kerber, Sharath Raghvendra, “Polynomial-Sized Topological Approximations Using The Permutahedron”, in arXiv‎^[1]:

     This result stems from high-dimensional lattice geometry and exploits properties of the permutahedral lattice, a well-studied structure in discrete geometry. Building on the same geometric concept, we also present a lower bound result on the size of an approximate filtration: we construct a point set for which every $(1+\epsilon )$-approximation of the \v{C}ech filtration has to contain $n^{\Omega (\log \log n)}$ features, provided that $\epsilon <{\frac {1}{\log ^{1+c}n}}$ for $c\in (0,1)$..