Matches in SemOpenAlex for { <https://semopenalex.org/work/W3033070411> ?p ?o ?g. }
Showing items 1 to 79 of
79
with 100 items per page.
- W3033070411 abstract "Let $G$ be a (multi) graph on the vertex set $V={0,1,ldots ,n}$ with root $0$. The $G$-parking function ideal $mathcal{M}_G$ is a monomial ideal in the polynomial ring $R=mathbb{K}[x_1,ldots ,x_n]$ over a field $mathbb{K}$ such that $dim_{mathbb K}left(frac{R}{mathcal{M}_G}right)=detleft(widetilde{L}_Gright)$, where $widetilde{L}_G$ is the truncated Laplace matrix of $G$ and $detleft(widetilde L_Gright)$ is the determinant of $widetilde L_G$. In other words, standard monomials of the Artinian quotient $frac{R}{mathcal{M}_G}$ correspond bijectively with the spanning trees of $G$. For $0leq kleq n-1$, the $k$-skeleton ideal $mathcal{M}_G^{(k)}$ of $G$ is the monomial subideal $mathcal{M}_G^{(k)}=leftlangle m_A:emptysetneq Asubseteq[n]text{ and }|A|leq k+1rightrangle$ of the $G$-parking function ideal $mathcal{M}_G=leftlangle m_A : emptyset neq Asubseteq[n]rightranglesubseteq R$. For a simple graph $G$, Dochtermann conjectured that $dim_{mathbb K}left(frac{R}{mathcal{M}_G^{(1)}}right)geqdetleft(widetilde{Q}_Gright)$, where $widetilde Q_G$ is the truncated signless Laplace matrix of $G$. We show that Dochtermann conjecture holds for any (simple or multi) graph $G$ on $V$." @default.
- W3033070411 created "2020-06-12" @default.
- W3033070411 creator A5022194843 @default.
- W3033070411 creator A5075235854 @default.
- W3033070411 creator A5085879106 @default.
- W3033070411 date "2020-06-03" @default.
- W3033070411 modified "2023-09-24" @default.
- W3033070411 title "Standard Monomials of 1-Skeleton Ideals of Graphs and Their Signless Laplace Matrices" @default.
- W3033070411 cites W1597381512 @default.
- W3033070411 cites W1644390119 @default.
- W3033070411 cites W1965605835 @default.
- W3033070411 cites W2017408364 @default.
- W3033070411 cites W3104774404 @default.
- W3033070411 hasPublicationYear "2020" @default.
- W3033070411 type Work @default.
- W3033070411 sameAs 3033070411 @default.
- W3033070411 citedByCount "1" @default.
- W3033070411 countsByYear W30330704112020 @default.
- W3033070411 crossrefType "posted-content" @default.
- W3033070411 hasAuthorship W3033070411A5022194843 @default.
- W3033070411 hasAuthorship W3033070411A5075235854 @default.
- W3033070411 hasAuthorship W3033070411A5085879106 @default.
- W3033070411 hasConcept C111472728 @default.
- W3033070411 hasConcept C11252640 @default.
- W3033070411 hasConcept C114614502 @default.
- W3033070411 hasConcept C132525143 @default.
- W3033070411 hasConcept C134306372 @default.
- W3033070411 hasConcept C138885662 @default.
- W3033070411 hasConcept C199422724 @default.
- W3033070411 hasConcept C2776639384 @default.
- W3033070411 hasConcept C2777789435 @default.
- W3033070411 hasConcept C2780990831 @default.
- W3033070411 hasConcept C2993105083 @default.
- W3033070411 hasConcept C33923547 @default.
- W3033070411 hasConcept C80899671 @default.
- W3033070411 hasConcept C90119067 @default.
- W3033070411 hasConcept C9485509 @default.
- W3033070411 hasConceptScore W3033070411C111472728 @default.
- W3033070411 hasConceptScore W3033070411C11252640 @default.
- W3033070411 hasConceptScore W3033070411C114614502 @default.
- W3033070411 hasConceptScore W3033070411C132525143 @default.
- W3033070411 hasConceptScore W3033070411C134306372 @default.
- W3033070411 hasConceptScore W3033070411C138885662 @default.
- W3033070411 hasConceptScore W3033070411C199422724 @default.
- W3033070411 hasConceptScore W3033070411C2776639384 @default.
- W3033070411 hasConceptScore W3033070411C2777789435 @default.
- W3033070411 hasConceptScore W3033070411C2780990831 @default.
- W3033070411 hasConceptScore W3033070411C2993105083 @default.
- W3033070411 hasConceptScore W3033070411C33923547 @default.
- W3033070411 hasConceptScore W3033070411C80899671 @default.
- W3033070411 hasConceptScore W3033070411C90119067 @default.
- W3033070411 hasConceptScore W3033070411C9485509 @default.
- W3033070411 hasLocation W30330704111 @default.
- W3033070411 hasOpenAccess W3033070411 @default.
- W3033070411 hasPrimaryLocation W30330704111 @default.
- W3033070411 hasRelatedWork W2162291589 @default.
- W3033070411 hasRelatedWork W2540609558 @default.
- W3033070411 hasRelatedWork W2581992092 @default.
- W3033070411 hasRelatedWork W2599725681 @default.
- W3033070411 hasRelatedWork W2618151668 @default.
- W3033070411 hasRelatedWork W2792150548 @default.
- W3033070411 hasRelatedWork W2915661044 @default.
- W3033070411 hasRelatedWork W2943841550 @default.
- W3033070411 hasRelatedWork W2952110075 @default.
- W3033070411 hasRelatedWork W2967496539 @default.
- W3033070411 hasRelatedWork W2972276614 @default.
- W3033070411 hasRelatedWork W3004073245 @default.
- W3033070411 hasRelatedWork W3010947672 @default.
- W3033070411 hasRelatedWork W3134311240 @default.
- W3033070411 hasRelatedWork W3159823729 @default.
- W3033070411 hasRelatedWork W3182016309 @default.
- W3033070411 hasRelatedWork W3200334570 @default.
- W3033070411 hasRelatedWork W2133518664 @default.
- W3033070411 hasRelatedWork W2613114488 @default.
- W3033070411 hasRelatedWork W3096673742 @default.
- W3033070411 isParatext "false" @default.
- W3033070411 isRetracted "false" @default.
- W3033070411 magId "3033070411" @default.
- W3033070411 workType "article" @default.