Matches in SemOpenAlex for { <https://semopenalex.org/work/W1738124807> ?p ?o ?g. }
Showing items 1 to 74 of
74
with 100 items per page.
- W1738124807 abstract "Let $C_{m,n}$ be the graph on the vertex set ${1, ldots, m} times {0, ldots, n-1}$ in which there is an edge between $(a,b)$ and $(c,d)$ if and only if either $(a,b) = (c,dpm 1)$ or $(a,b) = (c pm 1,d)$, where the second index is computed modulo $n$. One may view $C_{m,n}$ as a unit square grid on a cylinder with circumference $n$ units. For odd $n$, we prove that the Euler characteristic of the simplicial complex $Sigma_{m,n}$ of independent sets in $C_{m,n}$ is either $2$ or $-1$, depending on whether or not $gcd(m-1,n)$ is divisble by $3$. The proof relies heavily on previous work due to Thapper, who reduced the problem of computing the Euler characteristic of $Sigma_{m,n}$ to that of analyzing a certain subfamily of sets with attractive properties. The situation for even $n$ remains unclear. In the language of statistical mechanics, the reduced Euler characteristic of $Sigma_{m,n}$ coincides with minus the partition function of the corresponding hard square model with activity $-1$." @default.
- W1738124807 created "2016-06-24" @default.
- W1738124807 creator A5030076186 @default.
- W1738124807 date "2009-03-23" @default.
- W1738124807 modified "2023-10-18" @default.
- W1738124807 title "Hard Squares with Negative Activity on Cylinders with Odd Circumference" @default.
- W1738124807 cites W1520897746 @default.
- W1738124807 cites W1660697842 @default.
- W1738124807 cites W2070673991 @default.
- W1738124807 cites W2076483654 @default.
- W1738124807 cites W2089209018 @default.
- W1738124807 cites W2127719013 @default.
- W1738124807 cites W2157328819 @default.
- W1738124807 cites W2169447603 @default.
- W1738124807 doi "https://doi.org/10.37236/71" @default.
- W1738124807 hasPublicationYear "2009" @default.
- W1738124807 type Work @default.
- W1738124807 sameAs 1738124807 @default.
- W1738124807 citedByCount "13" @default.
- W1738124807 countsByYear W17381248072012 @default.
- W1738124807 countsByYear W17381248072013 @default.
- W1738124807 countsByYear W17381248072014 @default.
- W1738124807 countsByYear W17381248072016 @default.
- W1738124807 countsByYear W17381248072017 @default.
- W1738124807 countsByYear W17381248072023 @default.
- W1738124807 crossrefType "journal-article" @default.
- W1738124807 hasAuthorship W1738124807A5030076186 @default.
- W1738124807 hasBestOaLocation W17381248071 @default.
- W1738124807 hasConcept C114614502 @default.
- W1738124807 hasConcept C118615104 @default.
- W1738124807 hasConcept C132525143 @default.
- W1738124807 hasConcept C134306372 @default.
- W1738124807 hasConcept C166504685 @default.
- W1738124807 hasConcept C196433757 @default.
- W1738124807 hasConcept C2524010 @default.
- W1738124807 hasConcept C33923547 @default.
- W1738124807 hasConcept C42812 @default.
- W1738124807 hasConcept C54732982 @default.
- W1738124807 hasConcept C62884695 @default.
- W1738124807 hasConcept C7356347 @default.
- W1738124807 hasConcept C80899671 @default.
- W1738124807 hasConceptScore W1738124807C114614502 @default.
- W1738124807 hasConceptScore W1738124807C118615104 @default.
- W1738124807 hasConceptScore W1738124807C132525143 @default.
- W1738124807 hasConceptScore W1738124807C134306372 @default.
- W1738124807 hasConceptScore W1738124807C166504685 @default.
- W1738124807 hasConceptScore W1738124807C196433757 @default.
- W1738124807 hasConceptScore W1738124807C2524010 @default.
- W1738124807 hasConceptScore W1738124807C33923547 @default.
- W1738124807 hasConceptScore W1738124807C42812 @default.
- W1738124807 hasConceptScore W1738124807C54732982 @default.
- W1738124807 hasConceptScore W1738124807C62884695 @default.
- W1738124807 hasConceptScore W1738124807C7356347 @default.
- W1738124807 hasConceptScore W1738124807C80899671 @default.
- W1738124807 hasIssue "2" @default.
- W1738124807 hasLocation W17381248071 @default.
- W1738124807 hasLocation W17381248072 @default.
- W1738124807 hasOpenAccess W1738124807 @default.
- W1738124807 hasPrimaryLocation W17381248071 @default.
- W1738124807 hasRelatedWork W1738124807 @default.
- W1738124807 hasRelatedWork W2964340696 @default.
- W1738124807 hasRelatedWork W3004131592 @default.
- W1738124807 hasRelatedWork W3087852249 @default.
- W1738124807 hasRelatedWork W3187949862 @default.
- W1738124807 hasRelatedWork W4244487191 @default.
- W1738124807 hasRelatedWork W4295106960 @default.
- W1738124807 hasRelatedWork W4297779300 @default.
- W1738124807 hasRelatedWork W4301042201 @default.
- W1738124807 hasRelatedWork W4318434014 @default.
- W1738124807 hasVolume "16" @default.
- W1738124807 isParatext "false" @default.
- W1738124807 isRetracted "false" @default.
- W1738124807 magId "1738124807" @default.
- W1738124807 workType "article" @default.