Shellable complexes from multicomplexes

Shellable complexes from multicomplexes

Suppose a group G acts properly on a simplicial complex Γ . Let l be the number of G -invariant vertices, and p 1 , p 2 ,…, p m be the sizes of the G -orbits having size greater than 1. Then Γ must be a subcomplex of . A result of Novik gives necessary conditions on the face numbers of Cohen–Macaula...

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Veröffentlicht in:Journal of algebraic combinatorics 2010-08, Vol.32 (1), p.99-112
1. Verfasser: Browder, Jonathan
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Computer Science
Convex and Discrete Geometry
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
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Zusammenfassung:Suppose a group G acts properly on a simplicial complex Γ . Let l be the number of G -invariant vertices, and p 1 , p 2 ,…, p m be the sizes of the G -orbits having size greater than 1. Then Γ must be a subcomplex of . A result of Novik gives necessary conditions on the face numbers of Cohen–Macaulay subcomplexes of Λ . We show that these conditions are also sufficient, and thus provide a complete characterization of the face numbers of these complexes.
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-009-0206-z