permutahedralとは 意味・読み方・使い方

形容詞

permutahedral (not comparable)

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