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- Hilbert–Poincaré_series abstract "In mathematics, and in particular in the field of algebra, a Hilbert–Poincaré series (also known under the name Hilbert series), named after David Hilbert and Henri Poincaré, is an adaptation of the notion of dimension to the context of graded algebraic structures (where the dimension of the entire structure is often infinite). It is a formal power series in one indeterminate, say t, where the coefficient of tn gives the dimension (or rank) of the sub-structure of elements homogeneous of degree n. It is closely related to the Hilbert polynomial in cases when the latter exists; however, the Hilbert–Poincaré series describes the rank in every degree, while the Hilbert polynomial describes it only in all but finitely many degrees, and therefore provides less information. In particular the Hilbert–Poincaré series cannot be deduced from the Hilbert polynomial even if the latter exists. In good cases, the Hilbert–Poincaré series can be expressed as a rational function of its argument t.".
- Hilbert–Poincaré_series wikiPageID "17006296".
- Hilbert–Poincaré_series wikiPageLength "4760".
- Hilbert–Poincaré_series wikiPageOutDegree "22".
- Hilbert–Poincaré_series wikiPageRevisionID "641094690".
- Hilbert–Poincaré_series wikiPageWikiLink Algebra.
- Hilbert–Poincaré_series wikiPageWikiLink Artinian_ring.
- Hilbert–Poincaré_series wikiPageWikiLink Category:Abstract_algebra.
- Hilbert–Poincaré_series wikiPageWikiLink Category:Linear_algebra.
- Hilbert–Poincaré_series wikiPageWikiLink Category:Mathematical_series.
- Hilbert–Poincaré_series wikiPageWikiLink Chain_complex.
- Hilbert–Poincaré_series wikiPageWikiLink Cohomology.
- Hilbert–Poincaré_series wikiPageWikiLink Commutative_ring.
- Hilbert–Poincaré_series wikiPageWikiLink David_Hilbert.
- Hilbert–Poincaré_series wikiPageWikiLink Dimension.
- Hilbert–Poincaré_series wikiPageWikiLink Formal_power_series.
- Hilbert–Poincaré_series wikiPageWikiLink Free_module.
- Hilbert–Poincaré_series wikiPageWikiLink Graded_algebra.
- Hilbert–Poincaré_series wikiPageWikiLink Graded_module.
- Hilbert–Poincaré_series wikiPageWikiLink Graded_ring.
- Hilbert–Poincaré_series wikiPageWikiLink Graded_vector_space.
- Hilbert–Poincaré_series wikiPageWikiLink Henri_Poincaré.
- Hilbert–Poincaré_series wikiPageWikiLink Hilbert_polynomial.
- Hilbert–Poincaré_series wikiPageWikiLink Hilbert_series_and_Hilbert_polynomial.
- Hilbert–Poincaré_series wikiPageWikiLink Hilberts_syzygy_theorem.
- Hilbert–Poincaré_series wikiPageWikiLink Mathematics.
- Hilbert–Poincaré_series wikiPageWikiLink Projective_resolution.
- Hilbert–Poincaré_series wikiPageWikiLink Rational_function.
- Hilbert–Poincaré_series wikiPageWikiLink Resolution_(algebra).
- Hilbert–Poincaré_series wikiPageWikiLinkText "Hilbert–Poincaré series".
- Hilbert–Poincaré_series wikiPageWikiLinkText "Poincaré series".
- Hilbert–Poincaré_series wikiPageWikiLinkText "graded dimension".
- Hilbert–Poincaré_series hasPhotoCollection Hilbert–Poincaré_series.
- Hilbert–Poincaré_series wikiPageUsesTemplate Template:Unreferenced.
- Hilbert–Poincaré_series subject Category:Abstract_algebra.
- Hilbert–Poincaré_series subject Category:Linear_algebra.
- Hilbert–Poincaré_series subject Category:Mathematical_series.
- Hilbert–Poincaré_series type Thing.
- Hilbert–Poincaré_series comment "In mathematics, and in particular in the field of algebra, a Hilbert–Poincaré series (also known under the name Hilbert series), named after David Hilbert and Henri Poincaré, is an adaptation of the notion of dimension to the context of graded algebraic structures (where the dimension of the entire structure is often infinite).".
- Hilbert–Poincaré_series label "Hilbert–Poincaré series".
- Hilbert–Poincaré_series sameAs متسلسلات_هيلبرت–بوانكاريه.
- Hilbert–Poincaré_series sameAs ヒルベルト–ポアンカレ級数.
- Hilbert–Poincaré_series sameAs m.0415cx7.
- Hilbert–Poincaré_series sameAs Q5761255.
- Hilbert–Poincaré_series sameAs Q5761255.
- Hilbert–Poincaré_series wasDerivedFrom Hilbert–Poincaré_series?oldid=641094690.
- Hilbert–Poincaré_series isPrimaryTopicOf Hilbert–Poincaré_series.