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Sharp Minimax Gram-Determinant Asymptotics for Labelled Unit Decompositions of the Identity — arXiv:2610.10979

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.10979
License (as archived): CC0-1.0
Archived: 2026-10-09T06:28:34.409Z
SHA-256 of the archived text: 37647d0b00011a870a631088469e3e5dd5812fa64eaafc23edd13c15190b1a8f
Stable URL of this page: https://metraipolis.com/documento/dc_dbb87f2a2b11

How to cite

Sharp Minimax Gram-Determinant Asymptotics for Labelled Unit Decompositions of the Identity — arXiv:2610.10979 — arXiv (en), https://arxiv.org/abs/2610.10979 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_dbb87f2a2b11 (Metraipolis archive dc_dbb87f2a2b11, sha256 37647d0b00011a870a631088469e3e5dd5812fa64eaafc23edd13c15190b1a8f)

BibTeX

@misc{dcdbb87f2a2b11,
  title = {Sharp Minimax Gram-Determinant Asymptotics for Labelled Unit Decompositions of the Identity — arXiv:2610.10979},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.10979},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_dbb87f2a2b11; sha256 37647d0b00011a870a631088469e3e5dd5812fa64eaafc23edd13c15190b1a8f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.10979. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We show that González Merino and Schymura's Conjecture 4.8, a sufficient condition for Makai's reverse isodiametric conjecture, fails in all sufficiently large dimensions. Its three-dimensional case follows from Aliev's proof. Pełczyński and Szarek's construction for enclosing parallelepipeds implies this failure. Using random frames, we also determine the sharp exponential determinant guarantee for every fixed ratio greater than one between the number of vectors and the dimension.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Metric Geometry (math.MG) ; Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2610.10979 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T05:53:01.787Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).