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We study a graph-theoretic problem in the Penrose P2-graphs which are the dual graphs of Penrose tilings by kites and darts. Using substitutions, local isomorphism and other properties of Penrose tilings, we construct a family of arbitrarily large in
Externí odkaz:
http://arxiv.org/abs/2312.08262
Autor:
Porrier, Carole
Publikováno v:
EPTCS 403, 2024, pp. 156-163
Penrose tilings are the most famous aperiodic tilings, and they have been studied extensively. In particular, patterns composed with hexagons (H), boats (B) and stars (S) were soon exhibited and many physicists published on what they later called HBS
Externí odkaz:
http://arxiv.org/abs/2307.14011
Autor:
Fernique, Thomas, Porrier, Carole
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 26:3, Combinatorics (November 4, 2024) dmtcs:10764
Ammann bars are formed by segments (decorations) on the tiles of a tiling such that forming straight lines with them while tiling forces non-periodicity. Only a few cases are known, starting with Robert Ammann's observations on Penrose tiles, but the
Externí odkaz:
http://arxiv.org/abs/2205.13973
Autor:
Porrier, Carole1, Fernique, Thomas2
Publikováno v:
Discrete Mathematics & Theoretical Computer Science (DMTCS). 2024, Vol. 26 Issue 3, p1-24. 24p.
Publikováno v:
Master's thesis, École nationale de la statistique et de l'administration économique, Malakoff
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od______3063::8d73281ced8e62b65a9d9e5a86e09632
https://spire.sciencespo.fr/hdl:/2441/5l6uh8ogmqildh09h6m8g4434
https://spire.sciencespo.fr/hdl:/2441/5l6uh8ogmqildh09h6m8g4434