Matches in SemOpenAlex for { <https://semopenalex.org/work/W4297874339> ?p ?o ?g. }
Showing items 1 to 66 of
66
with 100 items per page.
- W4297874339 abstract "The Taylor-Socolar tilings are regular hexagonal tilings of the plane but are distinguished in being comprised of hexagons of two colors in an aperiodic way. We place the Taylor-Socolar tilings into an algebraic setting which allows one to see them directly as model sets and to understand the corresponding tiling hull along with its generic and singular parts. Although the tilings were originally obtained by matching rules and by substitution, our approach sets the tilings into the framework of a cut and project scheme and studies how the tilings relate to the corresponding internal space. The centers of the entire set of tiles of one tiling form a lattice $Q$ in the plane. If $X_Q$ denotes the set of all Taylor-Socolar tilings with centers on $Q$ then $X_Q$ forms a natural hull under the standard local topology of hulls and is a dynamical system for the action of $Q$. The $Q$-adic completion $bar{Q}$ of $Q$ is a natural factor of $X_Q$ and the natural mapping $X_Q longrightarrow bar{Q}$ is bijective except at a dense set of points of measure 0 in $bar{Q}$. We show that $X_Q$ consists of three LI classes under translation. Two of these LI classes are very small, namely countable $Q$-orbits in $X_Q$. The other is a minimal dynamical system which maps surjectively to $bar{Q}$ and which is variously $2:1$, $6:1$, and $12:1$ at the singular points. We further develop the formula of Socolar and Taylor (2011) that determines the parity of the tiles of a tiling in terms of the co-ordinates of its tile centers. Finally we show that the hull of the parity tilings can be identified with the hull $X_Q$; more precisely the two hulls are mutually locally derivable." @default.
- W4297874339 created "2022-10-01" @default.
- W4297874339 creator A5069432090 @default.
- W4297874339 creator A5078860848 @default.
- W4297874339 date "2012-07-26" @default.
- W4297874339 modified "2023-09-29" @default.
- W4297874339 title "Taylor-Socolar hexagonal tilings as model sets" @default.
- W4297874339 doi "https://doi.org/10.48550/arxiv.1207.6237" @default.
- W4297874339 hasPublicationYear "2012" @default.
- W4297874339 type Work @default.
- W4297874339 citedByCount "0" @default.
- W4297874339 crossrefType "posted-content" @default.
- W4297874339 hasAuthorship W4297874339A5069432090 @default.
- W4297874339 hasAuthorship W4297874339A5078860848 @default.
- W4297874339 hasBestOaLocation W42978743391 @default.
- W4297874339 hasConcept C104247578 @default.
- W4297874339 hasConcept C110729354 @default.
- W4297874339 hasConcept C114614502 @default.
- W4297874339 hasConcept C121332964 @default.
- W4297874339 hasConcept C134306372 @default.
- W4297874339 hasConcept C17825722 @default.
- W4297874339 hasConcept C178650486 @default.
- W4297874339 hasConcept C187691185 @default.
- W4297874339 hasConcept C21550011 @default.
- W4297874339 hasConcept C24424167 @default.
- W4297874339 hasConcept C24890656 @default.
- W4297874339 hasConcept C2524010 @default.
- W4297874339 hasConcept C2781204021 @default.
- W4297874339 hasConcept C33923547 @default.
- W4297874339 hasConcept C35908053 @default.
- W4297874339 hasConcept C43817857 @default.
- W4297874339 hasConcept C9376300 @default.
- W4297874339 hasConceptScore W4297874339C104247578 @default.
- W4297874339 hasConceptScore W4297874339C110729354 @default.
- W4297874339 hasConceptScore W4297874339C114614502 @default.
- W4297874339 hasConceptScore W4297874339C121332964 @default.
- W4297874339 hasConceptScore W4297874339C134306372 @default.
- W4297874339 hasConceptScore W4297874339C17825722 @default.
- W4297874339 hasConceptScore W4297874339C178650486 @default.
- W4297874339 hasConceptScore W4297874339C187691185 @default.
- W4297874339 hasConceptScore W4297874339C21550011 @default.
- W4297874339 hasConceptScore W4297874339C24424167 @default.
- W4297874339 hasConceptScore W4297874339C24890656 @default.
- W4297874339 hasConceptScore W4297874339C2524010 @default.
- W4297874339 hasConceptScore W4297874339C2781204021 @default.
- W4297874339 hasConceptScore W4297874339C33923547 @default.
- W4297874339 hasConceptScore W4297874339C35908053 @default.
- W4297874339 hasConceptScore W4297874339C43817857 @default.
- W4297874339 hasConceptScore W4297874339C9376300 @default.
- W4297874339 hasLocation W42978743391 @default.
- W4297874339 hasLocation W42978743392 @default.
- W4297874339 hasOpenAccess W4297874339 @default.
- W4297874339 hasPrimaryLocation W42978743391 @default.
- W4297874339 hasRelatedWork W1985762284 @default.
- W4297874339 hasRelatedWork W1999241746 @default.
- W4297874339 hasRelatedWork W2098493855 @default.
- W4297874339 hasRelatedWork W2188248099 @default.
- W4297874339 hasRelatedWork W2949477170 @default.
- W4297874339 hasRelatedWork W3037611219 @default.
- W4297874339 hasRelatedWork W3213562055 @default.
- W4297874339 hasRelatedWork W4288481479 @default.
- W4297874339 hasRelatedWork W4297874339 @default.
- W4297874339 hasRelatedWork W4320931267 @default.
- W4297874339 isParatext "false" @default.
- W4297874339 isRetracted "false" @default.
- W4297874339 workType "article" @default.