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On stars and links of shellable polytopal complexes

Authors
Journal
Journal of Combinatorial Theory Series A
0097-3165
Publisher
Elsevier
Publication Date
Volume
113
Issue
4
Identifiers
DOI: 10.1016/j.jcta.2005.05.001
Keywords
  • Shellability
  • Polytopal Complex
  • Line Shelling
  • Vertex Star
  • Vertex Link

Abstract

Abstract The vertex stars of shellable polytopal complexes are shown to be shellable. The link of a vertex v of a shellable polytopal complex is also shown to be shellable, provided that all facets of the star of v are simple polytopes, or (more generally) if there exists a shelling F 1 , … , F n of the star of v such that, for every 1 < j ⩽ n , the intersection of F j with the previous facets is an initial segment of a line shelling of the boundary complex of F j .

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