{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:39:02Z","timestamp":1787323142670,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["FE-340\/13-1"],"award-info":[{"award-number":["FE-340\/13-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004895","name":"European Social Fund","doi-asserted-by":"publisher","award":["EFOP-3.6.3-VEKOP-16-2017-00002"],"award-info":[{"award-number":["EFOP-3.6.3-VEKOP-16-2017-00002"]}],"id":[{"id":"10.13039\/501100004895","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003825","name":"Magyar Tudom\u00e1nyos Akad\u00e9mia","doi-asserted-by":"publisher","award":["LP2017-19\/2017"],"award-info":[{"award-number":["LP2017-19\/2017"]}],"id":[{"id":"10.13039\/501100003825","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011019","name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","doi-asserted-by":"publisher","award":["K116769"],"award-info":[{"award-number":["K116769"]}],"id":[{"id":"10.13039\/501100011019","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011019","name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","doi-asserted-by":"publisher","award":["K132696"],"award-info":[{"award-number":["K132696"]}],"id":[{"id":"10.13039\/501100011019","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011019","name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","doi-asserted-by":"publisher","award":["FK132060"],"award-info":[{"award-number":["FK132060"]}],"id":[{"id":"10.13039\/501100011019","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We study covering numbers and local covering numbers with respect to difference graphs and complete bipartite graphs. In particular, we show that in every cover of a Young diagram with $\\binom{2k}{k}$ steps with generalized rectangles, there is a row or a column in the diagram that is used by at least $k+1$ rectangles and prove that this is best possible. This answers two questions by Kim et al. [ European J. Combin., 86 (2020), 103074], namely, what is the local complete bipartite covering number of a difference graph, and is there a sequence of graphs with a constant local difference graph covering numbers and unbounded local complete bipartite covering numbers? We add to the study of these local covering numbers with a lower bound construction and some examples. Following Kim et al., we use the results on local covering numbers to provide lower and upper bounds for the local dimension of partially ordered sets of height 2. We discuss the local dimension of some posets related to Boolean lattices and show that the poset induced by the first two layers of the Boolean lattice has local dimension $(1 + o(1))\\log_2\\log_2 n$. We conclude with some remarks on covering numbers for digraphs and Ferrers dimension.<\/jats:p>","DOI":"10.1137\/20m1313684","type":"journal-article","created":{"date-parts":[[2021,5,4]],"date-time":"2021-05-04T11:52:04Z","timestamp":1620129124000},"page":"915-927","source":"Crossref","is-referenced-by-count":2,"title":["On Covering Numbers, Young Diagrams, and the Local Dimension of Posets"],"prefix":"10.1137","volume":"35","author":[{"given":"G\u00e1bor","family":"Dam\u00e1sdi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefan","family":"Felsner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ant\u00f3nio","family":"Gira\u0342o","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bal\u00e1zs","family":"Keszegh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Lewis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6154-7905","authenticated-orcid":true,"given":"D\u00e1niel T.","family":"Nagy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Torsten","family":"Ueckerdt","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,5,4]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"A. Aggarwal, M. M. Klawe, D. Lichtenstein, N. Linial, and A. Wigderson,\n                      Multi-layer grid embeddings\n                      , in Proceeding of the 26th Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, 1985, pp. 186-196.","DOI":"10.1109\/SFCS.1985.37"},{"key":"atypb2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11083-019-09485-4","volume":"36","author":"Barrera-Cruz F.","year":"2019","journal-title":"Order"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2006.04.003"},{"key":"atypb4","unstructured":"A. Bouchet,\n                      Etude combinatoire des ensembles ordonn\u00e9s finis\n                      , Doctoral thesis, Universite de Grenoble, 1971."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(82)90167-4"},{"key":"atypb6","unstructured":"D. Eppstein, J.C. Falmagne, and S. 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