{"publication_status":"published","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"doi":"10.1137/16M110407X","publisher":"Society for Industrial and Applied Mathematics","type":"journal_article","isi":1,"issue":"3","year":"2018","department":[{"_id":"HeEd"}],"article_processing_charge":"No","publication":"SIAM Journal on Discrete Mathematics","citation":{"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.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 32, no. 3, Society for Industrial and Applied Mathematics, 2018, pp. 2242–57, doi:<a href=\"https://doi.org/10.1137/16M110407X\">10.1137/16M110407X</a>.","ama":"Akopyan A, Segal Halevi E. Counting blanks in polygonal arrangements. <i>SIAM Journal on Discrete Mathematics</i>. 2018;32(3):2242-2257. doi:<a href=\"https://doi.org/10.1137/16M110407X\">10.1137/16M110407X</a>","ieee":"A. Akopyan and E. Segal Halevi, “Counting blanks in polygonal arrangements,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 32, no. 3. Society for Industrial and Applied Mathematics, pp. 2242–2257, 2018.","apa":"Akopyan, A., &#38; Segal Halevi, E. (2018). Counting blanks in polygonal arrangements. <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/16M110407X\">https://doi.org/10.1137/16M110407X</a>","chicago":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics, 2018. <a href=\"https://doi.org/10.1137/16M110407X\">https://doi.org/10.1137/16M110407X</a>.","short":"A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018) 2242–2257."},"external_id":{"arxiv":["1604.00960"],"isi":["000450810500036"]},"oa_version":"Preprint","day":"06","intvolume":"        32","date_updated":"2026-07-07T10:46:26Z","quality_controlled":"1","date_published":"2018-09-06T00:00:00Z","scopus_import":"1","publist_id":"7996","_id":"58","month":"09","project":[{"call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"arxiv":1,"title":"Counting blanks in polygonal arrangements","volume":32,"status":"public","page":"2242 - 2257","oa":1,"author":[{"last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","first_name":"Arseniy","orcid":"0000-0002-2548-617X"},{"first_name":"Erel","full_name":"Segal Halevi, Erel","last_name":"Segal Halevi"}],"main_file_link":[{"url":"https://arxiv.org/abs/1604.00960","open_access":"1"}],"abstract":[{"lang":"eng","text":"Inside a two-dimensional region (``cake&quot;&quot;), there are m nonoverlapping tiles of a certain kind (``toppings&quot;&quot;). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same ``certain kind,&quot;&quot; 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."}],"fulldoi":"https://doi.org/10.1137/16M110407X","date_created":"2018-12-11T11:44:24Z"}