---
res:
  bibo_abstract:
  - "We generalize a classical result by Boris Delaunay that introduced Delaunay triangulations.
    In particular, we prove that for a locally finite and coarsely dense generic point
    set A in ℝ^d, every generic point of ℝ^d belongs to exactly binom(d+k,d) simplices
    whose vertices belong to A and whose circumspheres enclose exactly k points of
    A. We extend this result to the cases in which the points are weighted, and when
    A contains only finitely many points in ℝ^d or in \U0001D54A^d. Furthermore, we
    use the result to give a new geometric proof for the fact that volumes of hypersimplices
    are Eulerian numbers.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Herbert
      foaf_name: Edelsbrunner, Herbert
      foaf_surname: Edelsbrunner
      foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-9823-6833
  - foaf_Person:
      foaf_givenName: Alexey
      foaf_name: Garber, Alexey
      foaf_surname: Garber
  - foaf_Person:
      foaf_givenName: Morteza
      foaf_name: Saghafian, Morteza
      foaf_surname: Saghafian
      foaf_workInfoHomepage: http://www.librecat.org/personId=f86f7148-b140-11ec-9577-95435b8df824
  bibo_doi: 10.4230/LIPIcs.SoCG.2025.43
  bibo_volume: 332
  dct_date: 2025^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1868-8969
  - http://id.crossref.org/issn/9783959773706
  dct_language: eng
  dct_publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik@
  dct_title: On spheres with k points inside@
...