{"external_id":{"arxiv":["1604.00960"]},"publication":"SIAM Journal on Discrete Mathematics","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"first_name":"Erel","full_name":"Segal Halevi, Erel","last_name":"Segal Halevi"}],"department":[{"_id":"HeEd"}],"page":"2242 - 2257","doi":"10.1137/16M110407X","type":"journal_article","date_updated":"2021-01-12T08:03:33Z","title":"Counting blanks in polygonal arrangements","citation":{"ama":"Akopyan A, Segal Halevi E. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 2018;32(3):2242-2257. 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.","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.","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.","short":"A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018) 2242–2257.","ista":"Akopyan A, Segal Halevi E. 2018. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 32(3), 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"},"ec_funded":1,"issue":"3","language":[{"iso":"eng"}],"publication_status":"published","quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1604.00960","open_access":"1"}],"oa_version":"Preprint","year":"2018","_id":"58","month":"09","day":"06","scopus_import":1,"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"oa":1,"publist_id":"7996","volume":32,"status":"public","intvolume":" 32","date_published":"2018-09-06T00:00:00Z","publisher":"Society for Industrial and Applied Mathematics ","abstract":[{"text":"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.","lang":"eng"}],"date_created":"2018-12-11T11:44:24Z"}