{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,11]],"date-time":"2025-06-11T13:49:22Z","timestamp":1749649762024},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","funder":[{"name":"European Research Council","award":["681988"],"award-info":[{"award-number":["681988"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2021,8]]},"abstract":"<jats:p> Finite smooth digraphs, that is, finite directed graphs without sources and sinks, can be partially ordered via pp-constructability. We give a complete description of this poset and, in particular, we prove that it is a distributive lattice. Moreover, we show that in order to separate two smooth digraphs in our poset it suffices to show that the polymorphism clone of one of the digraphs satisfies a prime cyclic loop condition that is not satisfied by the polymorphism clone of the other. Furthermore, we prove that the poset of cyclic loop conditions ordered by their strength for clones is a distributive lattice, too. <\/jats:p>","DOI":"10.1142\/s0218196721500442","type":"journal-article","created":{"date-parts":[[2021,6,25]],"date-time":"2021-06-25T02:22:23Z","timestamp":1624587743000},"page":"929-967","source":"Crossref","is-referenced-by-count":5,"title":["Smooth digraphs modulo primitive positive constructability and cyclic loop conditions"],"prefix":"10.1142","volume":"31","author":[{"given":"Manuel","family":"Bodirsky","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Algebra, TU Dresden, Dresden 01062, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Florian","family":"Starke","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Algebra, TU Dresden, Dresden 01062, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Albert","family":"Vucaj","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Algebra, TU Dresden, Dresden 01062, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,6,24]]},"reference":[{"key":"S0218196721500442BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196713500215"},{"key":"S0218196721500442BIB003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-09-09883-9"},{"key":"S0218196721500442BIB004","series-title":"Dagstuhl Follow-Ups","first-page":"45","volume-title":"The Constraint Satisfaction Problem: Complexity and Approximability","volume":"7","author":"Barto L.","year":"2017"},{"key":"S0218196721500442BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-009-0025-z"},{"key":"S0218196721500442BIB006","doi-asserted-by":"publisher","DOI":"10.1137\/070708093"},{"key":"S0218196721500442BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-017-1621-9"},{"key":"S0218196721500442BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-020-0647-8"},{"key":"S0218196721500442BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2005.09.028"},{"key":"S0218196721500442BIB011","first-page":"319","volume-title":"58th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2017","author":"Bulatov A. 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