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Partition and Cohen...
Partition and Cohen-Macaulay extenders
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- Doolittle, Joseph (författare)
- Graz Univ Technol, Inst Geometry, Graz, Austria.
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- Goeckner, Bennet (författare)
- Univ Washington, Dept Math, Seattle, WA 98195 USA.
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- Lazar, Alexander (författare)
- KTH,Matematik (Inst.)
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Graz Univ Technol, Inst Geometry, Graz, Austria Univ Washington, Dept Math, Seattle, WA 98195 USA. (creator_code:org_t)
- Elsevier BV, 2022
- 2022
- Engelska.
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Ingår i: European journal of combinatorics (Print). - : Elsevier BV. - 0195-6698 .- 1095-9971. ; 102
- Relaterad länk:
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http://arxiv.org/pdf...
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visa fler...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- If a pure simplicial complex is partitionable, then its h-vector has a combinatorial interpretation in terms of any partitioning of the complex. Given a non-partitionable complex increment , we construct a complex Gamma superset of increment of the same dimension such that both Gamma and the relative complex (Gamma , increment ) are partitionable. This allows us to rewrite the h-vector of any pure simplicial complex as the difference of two h-vectors of partitionable complexes, giving an analogous interpretation of the h-vector of a non-partitionable complex. By contrast, for a given complex increment it is not always possible to find a complex Gamma such that both Gamma and (Gamma , increment ) are Cohen- Macaulay. We characterize when this is possible, and we show that the construction of such a Gamma in this case is remarkably straightforward. We end with a note on a similar notion for shellability and a connection to Simon's conjecture on extendable shellability for uniform matroids.
Ämnesord
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
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