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Antipodality of spherical designs with odd harmonic indices

Combinatorics 2026-01-06 v6 Metric Geometry

Abstract

We determine the smallest size of a non-antipodal spherical design with harmonic indices {1,3,,2m1}\{1,3,\dots,2m-1\} to be 2m+12m+1, where mm is a positive integer. This is achieved by proving an analogous result for interval designs.

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Cite

@article{arxiv.2410.09471,
  title  = {Antipodality of spherical designs with odd harmonic indices},
  author = {Ryutaro Misawa and Akihiro Munemasa and Masanori Sawa},
  journal= {arXiv preprint arXiv:2410.09471},
  year   = {2026}
}

Comments

corrected typo, 13 pages