---
res:
  bibo_abstract:
  - "The classical Steinitz theorem states that if the origin belongs to the interior
    of the convex hull of a set \U0001D446⊂ℝ\U0001D451, then there are at most 2\U0001D451
    points of \U0001D446 whose convex hull contains the origin in the interior. Bárány,
    Katchalski,and Pach proved the following quantitative version of Steinitz’s theorem.
    Let \U0001D444 be a convex polytope in ℝ\U0001D451 containing the standard Euclidean
    unit ball \U0001D401\U0001D451. Then there exist at most 2\U0001D451 vertices
    of \U0001D444 whose convex hull \U0001D444′ satisfies \U0001D45F\U0001D401\U0001D451⊂\U0001D444′
    with \U0001D45F⩾\U0001D451−2\U0001D451. They conjectured that \U0001D45F⩾\U0001D450\U0001D451−1∕2
    holds with a universal constant \U0001D450>0. We prove \U0001D45F⩾15\U0001D4512,
    the first polynomial lower bound on \U0001D45F. Furthermore, we show that \U0001D45F
    is not greater than 2/√\U0001D451.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Grigory
      foaf_name: Ivanov, Grigory
      foaf_surname: Ivanov
      foaf_workInfoHomepage: http://www.librecat.org/personId=87744F66-5C6F-11EA-AFE0-D16B3DDC885E
  - foaf_Person:
      foaf_givenName: Márton
      foaf_name: Naszódi, Márton
      foaf_surname: Naszódi
  bibo_doi: 10.1112/blms.12965
  bibo_issue: '2'
  bibo_volume: 56
  dct_date: 2024^xs_gYear
  dct_identifier:
  - UT:001113277100001
  dct_isPartOf:
  - http://id.crossref.org/issn/0024-6093
  - http://id.crossref.org/issn/1469-2120
  dct_language: eng
  dct_publisher: London Mathematical Society@
  dct_title: 'Quantitative Steinitz theorem: A polynomial bound@'
...