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- H-vector abstract "In algebraic combinatorics, the h-vector of a simplicial polytope is a fundamental invariant of the polytope which encodes the number of faces of different dimensions and allows one to express the Dehn–Sommerville equations in a particularly simple form. A characterization of the set of h-vectors of simplicial polytopes was conjectured by Peter McMullen and proved by Lou Billera and Carl W. Lee and Richard Stanley (g-theorem). The definition of h-vector applies to arbitrary abstract simplicial complexes. The g-conjecture states that for simplicial spheres, all possible h-vectors occur already among the h-vectors of the boundaries of convex simplicial polytopes.Stanley introduced a generalization of the h-vector, the toric h-vector, which is defined for an arbitrary ranked poset, and proved that for the class of Eulerian posets, the Dehn–Sommerville equations continue to hold. A different, more combinatorial, generalization of the h-vector that has been extensively studied is the flag h-vector of a ranked poset. For Eulerian posets, it can be more concisely expressed by means of a noncommutative polynomial in two variables called the cd-index.".
- H-vector wikiPageExternalLink ec.
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- H-vector wikiPageRevisionID "676691067".
- H-vector wikiPageWikiLink Abstract_simplicial_complex.
- H-vector wikiPageWikiLink Algebraic_combinatorics.
- H-vector wikiPageWikiLink Category:Algebraic_combinatorics.
- H-vector wikiPageWikiLink Category:Polyhedral_combinatorics.
- H-vector wikiPageWikiLink Dehn–Sommerville_equations.
- H-vector wikiPageWikiLink Ehrhart_polynomial.
- H-vector wikiPageWikiLink Eulerian_poset.
- H-vector wikiPageWikiLink Finitely_generated_algebra.
- H-vector wikiPageWikiLink G-conjecture.
- H-vector wikiPageWikiLink G-theorem.
- H-vector wikiPageWikiLink Glossary_of_order_theory.
- H-vector wikiPageWikiLink Graded_algebra.
- H-vector wikiPageWikiLink Graded_poset.
- H-vector wikiPageWikiLink Graded_ring.
- H-vector wikiPageWikiLink Hilbert–Poincaré_series.
- H-vector wikiPageWikiLink Inclusion–exclusion_principle.
- H-vector wikiPageWikiLink Intersection_cohomology.
- H-vector wikiPageWikiLink Intersection_homology.
- H-vector wikiPageWikiLink Krull_dimension.
- H-vector wikiPageWikiLink Louis_Billera.
- H-vector wikiPageWikiLink Maximal_chain.
- H-vector wikiPageWikiLink Order_complex.
- H-vector wikiPageWikiLink Peter_McMullen.
- H-vector wikiPageWikiLink Poincaré_duality.
- H-vector wikiPageWikiLink Poset_topology.
- H-vector wikiPageWikiLink Projective_variety.
- H-vector wikiPageWikiLink Ranked_poset.
- H-vector wikiPageWikiLink Richard_P._Stanley.
- H-vector wikiPageWikiLink Simplicial_polytope.
- H-vector wikiPageWikiLink Simplicial_sphere.
- H-vector wikiPageWikiLink Stanley–Reisner_ring.
- H-vector wikiPageWikiLink Toric_variety.
- H-vector wikiPageWikiLinkText "''h''-vector".
- H-vector wikiPageWikiLinkText "''h''-vector''".
- H-vector wikiPageWikiLinkText "''h''-vectors".
- H-vector wikiPageWikiLinkText "h-vector".
- H-vector hasPhotoCollection H-vector.
- H-vector wikiPageUsesTemplate Template:Citation.
- H-vector wikiPageUsesTemplate Template:Lowercase.
- H-vector wikiPageUsesTemplate Template:Reflist.
- H-vector subject Category:Algebraic_combinatorics.
- H-vector subject Category:Polyhedral_combinatorics.
- H-vector hypernym Invariant.
- H-vector type Combinatoric.
- H-vector type Polytope.
- H-vector comment "In algebraic combinatorics, the h-vector of a simplicial polytope is a fundamental invariant of the polytope which encodes the number of faces of different dimensions and allows one to express the Dehn–Sommerville equations in a particularly simple form. A characterization of the set of h-vectors of simplicial polytopes was conjectured by Peter McMullen and proved by Lou Billera and Carl W. Lee and Richard Stanley (g-theorem).".
- H-vector label "H-vector".
- H-vector sameAs m.0bmfbw4.
- H-vector sameAs Q5627866.
- H-vector sameAs Q5627866.
- H-vector wasDerivedFrom H-vector?oldid=676691067.
- H-vector isPrimaryTopicOf H-vector.