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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.
- H-vector wikiPageID "11503563".
- H-vector wikiPageRevisionID "580052616".
- H-vector hasPhotoCollection H-vector.
- H-vector subject Category:Algebraic_combinatorics.
- H-vector subject Category:Polyhedral_combinatorics.
- 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".
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- H-vector sameAs Q5627866.
- H-vector sameAs Q5627866.
- H-vector wasDerivedFrom H-vector?oldid=580052616.
- H-vector isPrimaryTopicOf H-vector.