Algebraic shifting and strongly edge decomposable complexes
Let $\Gamma$ be a simplicial complex with $n$ vertices, and let $\Delta (\Gamma)$ be either its exterior algebraic shifted complex or its symmetric algebraic shifted complex. If $\Gamma$ is a simplicial sphere, then it is known that (a) $\Delta (\Gamma)$ is pure and (b) $h$-vector of $\Gamma$ is sym...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2008-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/3652/pdf |
| _version_ | 1797270421507145728 |
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| author | Satoshi Murai |
| author_facet | Satoshi Murai |
| author_sort | Satoshi Murai |
| collection | DOAJ |
| description | Let $\Gamma$ be a simplicial complex with $n$ vertices, and let $\Delta (\Gamma)$ be either its exterior algebraic shifted complex or its symmetric algebraic shifted complex. If $\Gamma$ is a simplicial sphere, then it is known that (a) $\Delta (\Gamma)$ is pure and (b) $h$-vector of $\Gamma$ is symmetric. Kalai and Sarkaria conjectured that if $\Gamma$ is a simplicial sphere then its algebraic shifting also satisfies (c) $\Delta (\Gamma) \subset \Delta (C(n,d))$, where $C(n,d)$ is the boundary complex of the cyclic $d$-polytope with $n$ vertices. We show this conjecture for strongly edge decomposable spheres introduced by Nevo. We also show that any shifted simplicial complex satisfying (a), (b) and (c) is the algebraic shifted complex of some simplicial sphere. |
| first_indexed | 2024-04-25T02:04:00Z |
| format | Article |
| id | doaj.art-69bb7486b74a465b8fcf2eaab68867f2 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:04:00Z |
| publishDate | 2008-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-69bb7486b74a465b8fcf2eaab68867f22024-03-07T14:38:06ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502008-01-01DMTCS Proceedings vol. AJ,...Proceedings10.46298/dmtcs.36523652Algebraic shifting and strongly edge decomposable complexesSatoshi Murai0Department of Pure and Applied MathematicsLet $\Gamma$ be a simplicial complex with $n$ vertices, and let $\Delta (\Gamma)$ be either its exterior algebraic shifted complex or its symmetric algebraic shifted complex. If $\Gamma$ is a simplicial sphere, then it is known that (a) $\Delta (\Gamma)$ is pure and (b) $h$-vector of $\Gamma$ is symmetric. Kalai and Sarkaria conjectured that if $\Gamma$ is a simplicial sphere then its algebraic shifting also satisfies (c) $\Delta (\Gamma) \subset \Delta (C(n,d))$, where $C(n,d)$ is the boundary complex of the cyclic $d$-polytope with $n$ vertices. We show this conjecture for strongly edge decomposable spheres introduced by Nevo. We also show that any shifted simplicial complex satisfying (a), (b) and (c) is the algebraic shifted complex of some simplicial sphere.https://dmtcs.episciences.org/3652/pdfalgebraic shiftingsimplicial spheresthe strong lefschetz propertysqueezed spheres[math.math-co] mathematics [math]/combinatorics [math.co][info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Satoshi Murai Algebraic shifting and strongly edge decomposable complexes Discrete Mathematics & Theoretical Computer Science algebraic shifting simplicial spheres the strong lefschetz property squeezed spheres [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Algebraic shifting and strongly edge decomposable complexes |
| title_full | Algebraic shifting and strongly edge decomposable complexes |
| title_fullStr | Algebraic shifting and strongly edge decomposable complexes |
| title_full_unstemmed | Algebraic shifting and strongly edge decomposable complexes |
| title_short | Algebraic shifting and strongly edge decomposable complexes |
| title_sort | algebraic shifting and strongly edge decomposable complexes |
| topic | algebraic shifting simplicial spheres the strong lefschetz property squeezed spheres [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/3652/pdf |
| work_keys_str_mv | AT satoshimurai algebraicshiftingandstronglyedgedecomposablecomplexes |