{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:56:01Z","timestamp":1787324161715,"version":"build-2736575974"},"reference-count":14,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>Algorithmic decidability is established for two order-theoretic properties of downward closed subsets defined by finitely many obstructions in two infinite posets. The properties under consideration are (a) being atomic, i.e., not being decomposable as a union of two downward closed proper subsets or, equivalently, satisfying the joint embedding property; and (b) being well quasi-ordered. The two posets are (1) words over a finite alphabet under the consecutive subword ordering, and (2) finite permutations under the consecutive subpermutation ordering. Underpinning the four results are characterizations of atomicity and well quasi-order for the subpath ordering on paths of a finite directed graph.<\/jats:p>","DOI":"10.1137\/20m1338411","type":"journal-article","created":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T11:16:36Z","timestamp":1616498196000},"page":"495-520","source":"Crossref","is-referenced-by-count":3,"title":["Atomicity and Well Quasi-Order for Consecutive Orderings on Words and Permutations"],"prefix":"10.1137","volume":"35","author":[{"given":"M.","family":"McDevitt","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2415-9334","authenticated-orcid":true,"given":"N.","family":"Ru\u0161kuc","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,3,23]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2017.08.001"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.03.079"},{"key":"atypb3","unstructured":"S. Braunfeld,\n                      Infinite Limits of Finite-Dimensional Permutation Structures, and Their Automorphism Groups: Between Model Theory and Combinatorics\n                      , Ph.D. dissertation, Rutgers University, 2018,https:\/\/arxiv.org\/abs\/1805.04219."},{"key":"atypb4","first-page":"9","volume":"21","author":"Braunfeld S.","year":"2019","journal-title":"Discrete Math. Theor. Comput. Sci."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.03.014"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2018.04.007"},{"key":"atypb7","first-page":"601","volume":"159","author":"Elizalde S.","year":"2016","journal-title":"IMA"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.326"},{"key":"atypb9","doi-asserted-by":"crossref","unstructured":"S. Huczynska and N. Ru\u0161kuc,\n                      Well quasi-order in combinatorics: Embeddings and homomorphisms\n                      , in Surveys in Combinatorics 2015, London Math. Soc. Lecture Note Ser. 424, Cambridge University Press, 2015, pp. 261-293.","DOI":"10.1017\/CBO9781316106853.009"},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"V. Jel\u00ednek,\n                      Ramsey-type and amalgamation-type properties of permutations\n                      , in Surveys in Combinatorics 2017, London Math. Soc. Lecture Note Ser. 440, Cambridge University Press, 2017, pp. 272-311.","DOI":"10.1017\/9781108332699.007"},{"key":"atypb11","unstructured":"M. McDevitt,\n                      Orderings on Words and Permutations\n                      , Ph.D. thesis, University of St Andrews, 2019."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2004.08.001"},{"key":"atypb13","unstructured":"J.H. van Lint and R.M. Wilson,\n                      A Course in Combinatorics\n                      , Cambridge University Press, 1992."},{"key":"atypb14","unstructured":"V. Vatter,\n                      Permutation classes\n                      , in Handbook of Enumerative Combinatorics, Discrete Math. Appl. (Boca Raton), CRC Press, 2015, pp. 753-833,https:\/\/arxiv.org\/abs\/1409.5159."}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1338411","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:19:36Z","timestamp":1787321976000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1338411"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1338411"],"URL":"https:\/\/doi.org\/10.1137\/20m1338411","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}