{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T22:00:37Z","timestamp":1780783237094,"version":"3.54.1"},"reference-count":11,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T00:00:00Z","timestamp":1779321600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Approximate Reasoning"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.ijar.2026.109726","type":"journal-article","created":{"date-parts":[[2026,5,24]],"date-time":"2026-05-24T05:44:59Z","timestamp":1779601499000},"page":"109726","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Lattices of integer partitions are almost subdirectly indecomposable"],"prefix":"10.1016","volume":"197","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0050-8085","authenticated-orcid":false,"given":"Mike","family":"Behrisch","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9677-9087","authenticated-orcid":false,"given":"Edith","family":"Vargas-Garc\u00eda","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6317-787X","authenticated-orcid":false,"given":"Andreas","family":"Wachtel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.ijar.2026.109726_bib0001","doi-asserted-by":"crossref","first-page":"109244:1","DOI":"10.1016\/j.ijar.2024.109244","article-title":"Arrow relations in lattices of integer partitions","volume":"172","author":"Almazaydeh","year":"2024","journal-title":"Internat. J. Approx. Reason."},{"key":"10.1016\/j.ijar.2026.109726_bib0002","series-title":"Formal Concept Analysis \u2013 16th International Conference, ICFCA 2021, Strasbourg, France, June 29 \u2013 July 2, 2021, Proceedings","first-page":"3","article-title":"Representing partition lattices through FCA","volume":"12733","author":"Behrisch","year":"2021"},{"key":"10.1016\/j.ijar.2026.109726_bib0003","unstructured":"M. Behrisch, E. Vargas-Garc\u00eda, A. Wachtel, Standard contexts and arrow-closed subcontexts of integer partition lattices, 2026. https:\/\/doi.org\/10.5281\/zenodo.18895342."},{"issue":"3","key":"10.1016\/j.ijar.2026.109726_bib0004","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/0012-365X(73)90094-0","article-title":"The lattice of integer partitions","volume":"6","author":"Brylawski","year":"1973","journal-title":"Discrete Math."},{"key":"10.1016\/j.ijar.2026.109726_bib0005","series-title":"15th International Conference on Concept Lattices and Their Applications","first-page":"19","article-title":"Notes on integer partitions","volume":"2668","author":"Ganter","year":"2020"},{"key":"10.1016\/j.ijar.2026.109726_bib0006","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.ijar.2021.11.004","article-title":"Notes on integer partitions","volume":"142","author":"Ganter","year":"2022","journal-title":"Internat. J. Approx. Reason."},{"key":"10.1016\/j.ijar.2026.109726_bib0007","series-title":"Formal concept analysis. Mathematical foundations","author":"Ganter","year":"2024"},{"issue":"1","key":"10.1016\/j.ijar.2026.109726_bib0008","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1112\/plms\/s2-17.1.75","article-title":"Asymptotic formul\u00e6 in combinatory analysis","volume":"17","author":"Hardy","year":"1918","journal-title":"Proc. London Math. Soc. (2)"},{"issue":"1\u20132","key":"10.1016\/j.ijar.2026.109726_bib0009","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1016\/S0304-3975(00)00363-7","article-title":"Structure of some sand piles model","volume":"262","author":"Latapy","year":"2001","journal-title":"Theoret. Comput. Sci."},{"issue":"6","key":"10.1016\/j.ijar.2026.109726_bib0010","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1016\/j.disc.2008.02.002","article-title":"The lattice of integer partitions and its infinite extension","volume":"309","author":"Latapy","year":"2009","journal-title":"Discrete Math."},{"key":"10.1016\/j.ijar.2026.109726_bib0011","unstructured":"OEIS, Sequence A000041, in: N.J.A. Sloane, The on-line encyclopedia of integer sequences, OEIS Foundation, 2026, Last accessed: 11 May 2026, https:\/\/oeis.org\/A000041."}],"container-title":["International Journal of Approximate Reasoning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0888613X26001027?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0888613X26001027?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T21:55:46Z","timestamp":1780782946000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0888613X26001027"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":11,"alternative-id":["S0888613X26001027"],"URL":"https:\/\/doi.org\/10.1016\/j.ijar.2026.109726","relation":{},"ISSN":["0888-613X"],"issn-type":[{"value":"0888-613X","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Lattices of integer partitions are almost subdirectly indecomposable","name":"articletitle","label":"Article Title"},{"value":"International Journal of Approximate Reasoning","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ijar.2026.109726","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier Inc.","name":"copyright","label":"Copyright"}],"article-number":"109726"}}