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permutahedral

出典:『Wiktionary』 (2017/03/01 20:45 UTC 版)

permutahedral (not comparable)

(数学) 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 + ϵ ) {\displaystyle (1+\epsilon )} $(1+\epsilon )$ -approximation of the \v{C}ech filtration has to contain n Ω ( log ⁡ log ⁡ n ) {\displaystyle n^{\Omega (\log \log n)}} $n^{\Omega (\log \log n)}$ features, provided that ϵ < 1 log 1 + c ⁡ n {\displaystyle \epsilon <{\frac {1}{\log ^{1+c}n}}} $\epsilon <{\frac {1}{\log ^{1+c}n}}$ for c ∈ ( 0 , 1 ) {\displaystyle c\in (0,1)} $c\in (0,1)$ ..

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