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Algebra Comput."],"published-print":{"date-parts":[[2021,11]]},"abstract":"<jats:p>This paper concerns a number of diagram categories, namely the partition, planar partition, Brauer, partial Brauer, Motzkin and Temperley\u2013Lieb categories. If [Formula: see text] denotes any of these categories, and if [Formula: see text] is a fixed morphism, then an associative operation [Formula: see text] may be defined on [Formula: see text] by [Formula: see text]. The resulting semigroup [Formula: see text] is called a sandwich semigroup. We conduct a thorough investigation of these sandwich semigroups, with an emphasis on structural and combinatorial properties such as Green\u2019s relations and preorders, regularity, stability, mid-identities, ideal structure, (products of) idempotents, and minimal generation. It turns out that the Brauer category has many remarkable properties not shared by any of the other diagram categories we study. Because of these unique properties, we may completely classify isomorphism classes of sandwich semigroups in the Brauer category, calculate the rank (smallest size of a generating set) of an arbitrary sandwich semigroup, enumerate Green\u2019s classes and idempotents, and calculate ranks (and idempotent ranks, where appropriate) of the regular subsemigroup and its ideals, as well as the idempotent-generated subsemigroup. Several illustrative examples are considered throughout, partly to demonstrate the sometimes-subtle differences between the various diagram categories.<\/jats:p>","DOI":"10.1142\/s021819672150048x","type":"journal-article","created":{"date-parts":[[2021,8,16]],"date-time":"2021-08-16T09:09:37Z","timestamp":1629104977000},"page":"1339-1404","source":"Crossref","is-referenced-by-count":6,"title":["Sandwich semigroups in diagram categories"],"prefix":"10.1142","volume":"31","author":[{"given":"Igor","family":"Dolinka","sequence":"first","affiliation":[{"name":"Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ivana","family":"\u0110ur\u0111ev","sequence":"additional","affiliation":[{"name":"Mathematical Institute of the Serbian Academy of Sciences and Arts, Beograd, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James","family":"East","sequence":"additional","affiliation":[{"name":"Centre for Research in Mathematics and Data Science, Western Sydney University, Sydney, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,8,13]]},"reference":[{"key":"S021819672150048XBIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF02389143"},{"key":"S021819672150048XBIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2013.09.010"},{"key":"S021819672150048XBIB004","doi-asserted-by":"publisher","DOI":"10.1017\/S030821050002607X"},{"key":"S021819672150048XBIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216502001524"},{"key":"S021819672150048XBIB006","doi-asserted-by":"publisher","DOI":"10.2307\/1968843"},{"key":"S021819672150048XBIB007","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1955-023-2"},{"key":"S021819672150048XBIB008","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(79)90130-4"},{"key":"S021819672150048XBIB009","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/007.1"},{"key":"S021819672150048XBIB010","doi-asserted-by":"publisher","DOI":"10.1142\/S021819671550037X"},{"key":"S021819672150048XBIB011","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-017-9873-6"},{"key":"S021819672150048XBIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2014.11.008"},{"key":"S021819672150048XBIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2016.09.018"},{"issue":"3","key":"S021819672150048XBIB014","first-page":"35","volume":"79","author":"Dolinka I.","year":"2018","journal-title":"Algebra Universalis"},{"issue":"3","key":"S021819672150048XBIB015","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/s00012-018-0533-9","volume":"79","author":"Dolinka I.","year":"2018","journal-title":"Algebra Universalis"},{"key":"S021819672150048XBIB016","doi-asserted-by":"publisher","DOI":"10.1142\/S021819671100611X"},{"key":"S021819672150048XBIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2016.09.001"},{"key":"S021819672150048XBIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2018.05.016"},{"key":"S021819672150048XBIB020","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972710001851"},{"key":"S021819672150048XBIB021","doi-asserted-by":"publisher","DOI":"10.1007\/BF03025769"},{"key":"S021819672150048XBIB022","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210505000636"},{"key":"S021819672150048XBIB023","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091504001397"},{"key":"S021819672150048XBIB024","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-013-9521-8"},{"key":"S021819672150048XBIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2004.06.005"},{"key":"S021819672150048XBIB026","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500004442"},{"key":"S021819672150048XBIB027","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700010339"},{"key":"S021819672150048XBIB028","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-41.1.707"},{"key":"S021819672150048XBIB029","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500010647"},{"key":"S021819672150048XBIB030","series-title":"London Mathematical Society Monographs. 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