---
res:
  bibo_abstract:
  - The depth of a cell in an arrangement of n (non-vertical) great-spheres in Sd
    is the number of great-spheres that pass above the cell. We prove Euler-type relations,
    which imply extensions of the classic Dehn–Sommerville relations for convex polytopes
    to sublevel sets of the depth function, and we use the relations to extend the
    expressions for the number of faces of neighborly polytopes to the number of cells
    of levels in neighborly arrangements.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Ranita
      foaf_name: Biswas, Ranita
      foaf_surname: Biswas
      foaf_workInfoHomepage: http://www.librecat.org/personId=3C2B033E-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-5372-7890
  - foaf_Person:
      foaf_givenName: Sebastiano
      foaf_name: Cultrera di Montesano, Sebastiano
      foaf_surname: Cultrera di Montesano
      foaf_workInfoHomepage: http://www.librecat.org/personId=34D2A09C-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0001-6249-0832
  - 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: Morteza
      foaf_name: Saghafian, Morteza
      foaf_surname: Saghafian
      foaf_workInfoHomepage: http://www.librecat.org/personId=f86f7148-b140-11ec-9577-95435b8df824
  dct_date: 2022^xs_gYear
  dct_language: eng
  dct_publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik@
  dct_title: 'Depth in arrangements: Dehn–Sommerville–Euler relations with applications@'
...