{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T18:11:02Z","timestamp":1648577462554},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2018,12]]},"abstract":"<jats:p> It is shown that the lattices of flats of boolean representable simplicial complexes are always atomistic, but semimodular if and only if the complex is a matroid. A canonical construction is introduced for arbitrary finite atomistic lattices, providing a characterization of the lattices of flats of boolean representable simplicial complexes and a decidability condition. We remark that every finite lattice occurs as the lattice of flats of some simplicial complex. <\/jats:p>","DOI":"10.1142\/s0218196718400131","type":"journal-article","created":{"date-parts":[[2018,8,20]],"date-time":"2018-08-20T06:57:53Z","timestamp":1534748273000},"page":"1677-1691","source":"Crossref","is-referenced-by-count":0,"title":["The lattice of flats of a boolean representable simplicial complex"],"prefix":"10.1142","volume":"28","author":[{"given":"Stuart","family":"Margolis","sequence":"first","affiliation":[{"name":"Department of Mathematics, Bar Ilan University, 52900 Ramat Gan, Israel"}]},{"given":"John","family":"Rhodes","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of California, Berkeley, California 94720, USA"}]},{"given":"Pedro V.","family":"Silva","sequence":"additional","affiliation":[{"name":"Centro de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade do Porto, R. Campo Alegre, 687, 4169-007 Porto, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2019,1,14]]},"reference":[{"key":"S0218196718400131BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-0018-1"},{"key":"S0218196718400131BIB002","doi-asserted-by":"publisher","DOI":"10.1080\/00927870802466967"},{"key":"S0218196718400131BIB006","doi-asserted-by":"publisher","DOI":"10.1080\/00927870902828793"},{"key":"S0218196718400131BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2010.04.007"},{"key":"S0218196718400131BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-011-0036-2"},{"key":"S0218196718400131BIB010","volume-title":"Matroid Theory","author":"Oxley J. G.","year":"1992"},{"key":"S0218196718400131BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/BF02482893"},{"key":"S0218196718400131BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-15114-4"},{"key":"S0218196718400131BIB013","volume-title":"An Introduction to Algebraic Topology","author":"Rotman J. J.","year":"1986"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196718400131","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T01:41:49Z","timestamp":1565142109000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196718400131"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12]]},"references-count":9,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2019,1,14]]},"published-print":{"date-parts":[[2018,12]]}},"alternative-id":["10.1142\/S0218196718400131"],"URL":"https:\/\/doi.org\/10.1142\/s0218196718400131","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12]]}}}