[{"date_created":"2018-12-11T11:44:24Z","date_published":"2018-09-06T00:00:00Z","uri_base":"https://research-explorer.ista.ac.at","page":"2242 - 2257","publication":"SIAM Journal on Discrete Mathematics","dc":{"identifier":["https://research-explorer.ista.ac.at/record/58"],"description":["Inside a two-dimensional region (``cake""), there are m nonoverlapping tiles of a certain kind (``toppings""). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same ``certain kind,"" such that the entire cake is covered. How many blanks must we add? We study this question in several cases: (1) The cake and toppings are general polygons. (2) The cake and toppings are convex figures. (3) The cake and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear polygon and the toppings are axis-parallel rectangles. In all four cases, we provide tight bounds on the number of blanks."],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1137/16M110407X","info:eu-repo/semantics/altIdentifier/wos/000450810500036","info:eu-repo/semantics/altIdentifier/arxiv/1604.00960","info:eu-repo/grantAgreement/EC/FP7/291734"],"source":["Akopyan A, Segal Halevi E. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 2018;32(3):2242-2257. doi:10.1137/16M110407X"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"],"publisher":["Society for Industrial and Applied Mathematics "],"date":["2018"],"creator":["Akopyan, Arseniy","Segal Halevi, Erel"],"language":["eng"],"rights":["info:eu-repo/semantics/openAccess"],"title":["Counting blanks in polygonal arrangements"]},"day":"06","isi":1,"oa":1,"quality_controlled":"1","external_id":{"isi":[],"arxiv":[]},"article_processing_charge":"No","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X"},{"last_name":"Segal Halevi","first_name":"Erel"}],"publist_id":"7996","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","dini_type":"doc-type:article","citation":{"chicago":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M110407X.","ista":"Akopyan A, Segal Halevi E. 2018. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 32(3), 2242–2257.","mla":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” SIAM Journal on Discrete Mathematics, vol. 32, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 2242–57, doi:10.1137/16M110407X.","ieee":"A. Akopyan and E. Segal Halevi, “Counting blanks in polygonal arrangements,” SIAM Journal on Discrete Mathematics, vol. 32, no. 3. Society for Industrial and Applied Mathematics , pp. 2242–2257, 2018.","short":"A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018) 2242–2257.","apa":"Akopyan, A., & Segal Halevi, E. (2018). Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/16M110407X"},"project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"issue":"3","volume":32,"language":[{}],"publication_status":"published","intvolume":" 32","month":"09","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1604.00960"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"lang":"eng"}],"department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"HeEd"}],"creator":{"id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","login":"dernst"},"date_updated":"2023-09-11T12:48:39Z","status":"public","type":"journal_article","_id":"58"}]