{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:28:01Z","timestamp":1760243281193,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2014,6,27]],"date-time":"2014-06-27T00:00:00Z","timestamp":1403827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs and decompositions of the pinned rigidity matrix. Many mechanisms have initial configurations, which are symmetric, and other recent work has exploited the orbit matrix as a symmetry adapted form of the rigidity matrix. This paper explores how the decomposition and analysis of symmetric frameworks and their symmetric motions can be supported by the new symmetry adapted tools.<\/jats:p>","DOI":"10.3390\/sym6030516","type":"journal-article","created":{"date-parts":[[2014,6,27]],"date-time":"2014-06-27T11:23:16Z","timestamp":1403868196000},"page":"516-550","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Symmetry Adapted Assur Decompositions"],"prefix":"10.3390","volume":"6","author":[{"given":"Anthony","family":"Nixon","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bernd","family":"Schulze","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adnan","family":"Sljoka","sequence":"additional","affiliation":[{"name":"Department of Physics, Ryerson University, Toronto, ON M5B 2K3, Canada"},{"name":"Department of Psychology and Neuroscience, University of Colorado, Boulder, CO 80309, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Walter","family":"Whiteley","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,6,27]]},"reference":[{"key":"ref_1","unstructured":"Artobolevski, I.I. 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