Matches in SemOpenAlex for { <https://semopenalex.org/work/W4200633303> ?p ?o ?g. }
Showing items 1 to 65 of
65
with 100 items per page.
- W4200633303 abstract "In 1999 Herzog and Hibi introduced componentwise linear ideals. A homogeneous ideal $I$ is componentwise linear if for all non-negative integers $d$, the ideal generated by the homogeneous elements of degree $d$ in $I$ has a linear resolution. For square-free monomial ideals, componentwise linearity is related via Alexander duality to the property of being sequentially Cohen-Macaulay for the corresponding simplicial complexes. In general, the property of being componentwise linear is not preserved by taking powers. In 2011, Herzog, Hibi, and Ohsugi conjectured that if $I$ is the cover ideal of a chordal graph, then $I^s$ is componentwise linear for all $s geq 1$. We survey some of the basic properties of componentwise linear ideals, and then specialize to the progress on the Herzog-Hibi-Ohsugi conjecture during the last decade. We also survey the related problem of determining when the symbolic powers of a cover ideal are componentwise linear." @default.
- W4200633303 created "2021-12-31" @default.
- W4200633303 creator A5025446621 @default.
- W4200633303 creator A5065706599 @default.
- W4200633303 date "2021-12-06" @default.
- W4200633303 modified "2023-09-27" @default.
- W4200633303 title "Powers of componentwise linear ideals: The Herzog--Hibi--Ohsugi Conjecture and related problems" @default.
- W4200633303 doi "https://doi.org/10.48550/arxiv.2112.03050" @default.
- W4200633303 hasPublicationYear "2021" @default.
- W4200633303 type Work @default.
- W4200633303 citedByCount "0" @default.
- W4200633303 crossrefType "posted-content" @default.
- W4200633303 hasAuthorship W4200633303A5025446621 @default.
- W4200633303 hasAuthorship W4200633303A5065706599 @default.
- W4200633303 hasBestOaLocation W42006333031 @default.
- W4200633303 hasConcept C11252640 @default.
- W4200633303 hasConcept C114614502 @default.
- W4200633303 hasConcept C118615104 @default.
- W4200633303 hasConcept C127413603 @default.
- W4200633303 hasConcept C134306372 @default.
- W4200633303 hasConcept C17744445 @default.
- W4200633303 hasConcept C199539241 @default.
- W4200633303 hasConcept C202444582 @default.
- W4200633303 hasConcept C2776639384 @default.
- W4200633303 hasConcept C2777789435 @default.
- W4200633303 hasConcept C2780428219 @default.
- W4200633303 hasConcept C2780990831 @default.
- W4200633303 hasConcept C33923547 @default.
- W4200633303 hasConcept C66882249 @default.
- W4200633303 hasConcept C78519656 @default.
- W4200633303 hasConcept C90119067 @default.
- W4200633303 hasConcept C9485509 @default.
- W4200633303 hasConceptScore W4200633303C11252640 @default.
- W4200633303 hasConceptScore W4200633303C114614502 @default.
- W4200633303 hasConceptScore W4200633303C118615104 @default.
- W4200633303 hasConceptScore W4200633303C127413603 @default.
- W4200633303 hasConceptScore W4200633303C134306372 @default.
- W4200633303 hasConceptScore W4200633303C17744445 @default.
- W4200633303 hasConceptScore W4200633303C199539241 @default.
- W4200633303 hasConceptScore W4200633303C202444582 @default.
- W4200633303 hasConceptScore W4200633303C2776639384 @default.
- W4200633303 hasConceptScore W4200633303C2777789435 @default.
- W4200633303 hasConceptScore W4200633303C2780428219 @default.
- W4200633303 hasConceptScore W4200633303C2780990831 @default.
- W4200633303 hasConceptScore W4200633303C33923547 @default.
- W4200633303 hasConceptScore W4200633303C66882249 @default.
- W4200633303 hasConceptScore W4200633303C78519656 @default.
- W4200633303 hasConceptScore W4200633303C90119067 @default.
- W4200633303 hasConceptScore W4200633303C9485509 @default.
- W4200633303 hasLocation W42006333031 @default.
- W4200633303 hasOpenAccess W4200633303 @default.
- W4200633303 hasPrimaryLocation W42006333031 @default.
- W4200633303 hasRelatedWork W1496720970 @default.
- W4200633303 hasRelatedWork W1633079080 @default.
- W4200633303 hasRelatedWork W1653027350 @default.
- W4200633303 hasRelatedWork W1964941796 @default.
- W4200633303 hasRelatedWork W1977013452 @default.
- W4200633303 hasRelatedWork W2005510300 @default.
- W4200633303 hasRelatedWork W2950419021 @default.
- W4200633303 hasRelatedWork W2951294841 @default.
- W4200633303 hasRelatedWork W2973213150 @default.
- W4200633303 hasRelatedWork W4301463618 @default.
- W4200633303 isParatext "false" @default.
- W4200633303 isRetracted "false" @default.
- W4200633303 workType "article" @default.