[{"article_type":"letter_note","oa_version":"Preprint","year":"2023","date_updated":"2023-10-04T11:54:57Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","external_id":{"arxiv":["2201.10892"]},"publication_identifier":{"issn":["0012-365X"]},"arxiv":1,"issue":"6","article_processing_charge":"No","article_number":"113363","abstract":[{"text":"The celebrated Erdős–Ko–Rado theorem about the maximal size of an intersecting family of r-element subsets of  was extended to the setting of exterior algebra in [5, Theorem 2.3] and in [6, Theorem 1.4]. However, the equality case has not been settled yet. In this short note, we show that the extension of the Erdős–Ko–Rado theorem and the characterization of the equality case therein, as well as those of the Hilton–Milner theorem to the setting of exterior algebra in the simplest non-trivial case of two-forms follow from a folklore puzzle about possible arrangements of an intersecting family of lines.","lang":"eng"}],"_id":"12680","date_published":"2023-06-01T00:00:00Z","publication_status":"published","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2201.10892","open_access":"1"}],"oa":1,"volume":346,"citation":{"apa":"Ivanov, G., &#38; Köse, S. (2023). Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. <i>Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.disc.2023.113363\">https://doi.org/10.1016/j.disc.2023.113363</a>","ama":"Ivanov G, Köse S. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. <i>Discrete Mathematics</i>. 2023;346(6). doi:<a href=\"https://doi.org/10.1016/j.disc.2023.113363\">10.1016/j.disc.2023.113363</a>","short":"G. Ivanov, S. Köse, Discrete Mathematics 346 (2023).","mla":"Ivanov, Grigory, and Seyda Köse. “Erdős-Ko-Rado and Hilton-Milner Theorems for Two-Forms.” <i>Discrete Mathematics</i>, vol. 346, no. 6, 113363, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.disc.2023.113363\">10.1016/j.disc.2023.113363</a>.","ieee":"G. Ivanov and S. Köse, “Erdős-Ko-Rado and Hilton-Milner theorems for two-forms,” <i>Discrete Mathematics</i>, vol. 346, no. 6. Elsevier, 2023.","ista":"Ivanov G, Köse S. 2023. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. Discrete Mathematics. 346(6), 113363.","chicago":"Ivanov, Grigory, and Seyda Köse. “Erdős-Ko-Rado and Hilton-Milner Theorems for Two-Forms.” <i>Discrete Mathematics</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.disc.2023.113363\">https://doi.org/10.1016/j.disc.2023.113363</a>."},"title":"Erdős-Ko-Rado and Hilton-Milner theorems for two-forms","day":"01","author":[{"id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory","first_name":"Grigory","last_name":"Ivanov"},{"first_name":"Seyda","full_name":"Köse, Seyda","last_name":"Köse","id":"8ba3170d-dc85-11ea-9058-c4251c96a6eb"}],"type":"journal_article","related_material":{"record":[{"id":"13331","relation":"dissertation_contains","status":"public"}]},"language":[{"iso":"eng"}],"doi":"10.1016/j.disc.2023.113363","month":"06","date_created":"2023-02-26T23:01:00Z","publisher":"Elsevier","quality_controlled":"1","department":[{"_id":"UlWa"},{"_id":"GradSch"}],"publication":"Discrete Mathematics","status":"public","intvolume":"       346"},{"publisher":"Elsevier","isi":1,"quality_controlled":"1","department":[{"_id":"UlWa"}],"publication":"Discrete Mathematics","intvolume":"       342","status":"public","page":"3201-3207","month":"11","date_created":"2019-07-14T21:59:20Z","project":[{"_id":"26366136-B435-11E9-9278-68D0E5697425","name":"Reglas de Conectividad funcional en el hipocampo"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"language":[{"iso":"eng"}],"doi":"10.1016/j.disc.2019.06.031","ec_funded":1,"citation":{"short":"A. Silva, A.M. Arroyo Guevara, B. Richter, O. Lee, Discrete Mathematics 342 (2019) 3201–3207.","ama":"Silva A, Arroyo Guevara AM, Richter B, Lee O. Graphs with at most one crossing. <i>Discrete Mathematics</i>. 2019;342(11):3201-3207. doi:<a href=\"https://doi.org/10.1016/j.disc.2019.06.031\">10.1016/j.disc.2019.06.031</a>","apa":"Silva, A., Arroyo Guevara, A. M., Richter, B., &#38; Lee, O. (2019). Graphs with at most one crossing. <i>Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.disc.2019.06.031\">https://doi.org/10.1016/j.disc.2019.06.031</a>","chicago":"Silva, André , Alan M Arroyo Guevara, Bruce Richter, and Orlando Lee. “Graphs with at Most One Crossing.” <i>Discrete Mathematics</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.disc.2019.06.031\">https://doi.org/10.1016/j.disc.2019.06.031</a>.","ista":"Silva A, Arroyo Guevara AM, Richter B, Lee O. 2019. Graphs with at most one crossing. Discrete Mathematics. 342(11), 3201–3207.","ieee":"A. Silva, A. M. Arroyo Guevara, B. Richter, and O. Lee, “Graphs with at most one crossing,” <i>Discrete Mathematics</i>, vol. 342, no. 11. Elsevier, pp. 3201–3207, 2019.","mla":"Silva, André, et al. “Graphs with at Most One Crossing.” <i>Discrete Mathematics</i>, vol. 342, no. 11, Elsevier, 2019, pp. 3201–07, doi:<a href=\"https://doi.org/10.1016/j.disc.2019.06.031\">10.1016/j.disc.2019.06.031</a>."},"title":"Graphs with at most one crossing","day":"01","author":[{"last_name":"Silva","full_name":"Silva, André ","first_name":"André "},{"id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2401-8670","full_name":"Arroyo Guevara, Alan M","first_name":"Alan M","last_name":"Arroyo Guevara"},{"last_name":"Richter","full_name":"Richter, Bruce","first_name":"Bruce"},{"first_name":"Orlando","full_name":"Lee, Orlando","last_name":"Lee"}],"type":"journal_article","publication_status":"published","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1901.09955","open_access":"1"}],"volume":342,"arxiv":1,"issue":"11","article_processing_charge":"No","date_published":"2019-11-01T00:00:00Z","_id":"6638","abstract":[{"lang":"eng","text":"The crossing number of a graph G is the least number of crossings over all possible drawings of G. We present a structural characterization of graphs with crossing number one."}],"date_updated":"2023-08-29T06:31:41Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000486358100025"],"arxiv":["1901.09955"]},"scopus_import":"1","publication_identifier":{"issn":["0012-365X"]},"year":"2019","oa_version":"Preprint"},{"year":"1990","oa_version":"None","publist_id":"2060","article_type":"original","publication_identifier":{"eissn":["1872-681X"],"issn":["0012-365X"]},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_updated":"2022-02-22T15:45:55Z","scopus_import":"1","abstract":[{"text":"We prove that given n⩾3 convex, compact, and pairwise disjoint sets in the plane, they may be covered with n non-overlapping convex polygons with a total of not more than 6n−9 sides, and with not more than 3n−6 distinct slopes. Furthermore, we construct sets that require 6n−9 sides and 3n−6 slopes for n⩾3. The upper bound on the number of slopes implies a new bound on a recently studied transversal problem.","lang":"eng"}],"_id":"4065","date_published":"1990-04-15T00:00:00Z","issue":"2","article_processing_charge":"No","volume":81,"main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/0012365X9090147A?via%3Dihub"}],"publication_status":"published","type":"journal_article","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Robison, Arch","first_name":"Arch","last_name":"Robison"},{"first_name":"Xiao","full_name":"Shen, Xiao","last_name":"Shen"}],"day":"15","title":"Covering convex sets with non-overlapping polygons","citation":{"chicago":"Edelsbrunner, Herbert, Arch Robison, and Xiao Shen. “Covering Convex Sets with Non-Overlapping Polygons.” <i>Discrete Mathematics</i>. Elsevier, 1990. <a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">https://doi.org/10.1016/0012-365X(90)90147-A</a>.","ista":"Edelsbrunner H, Robison A, Shen X. 1990. Covering convex sets with non-overlapping polygons. Discrete Mathematics. 81(2), 153–164.","ieee":"H. Edelsbrunner, A. Robison, and X. Shen, “Covering convex sets with non-overlapping polygons,” <i>Discrete Mathematics</i>, vol. 81, no. 2. Elsevier, pp. 153–164, 1990.","mla":"Edelsbrunner, Herbert, et al. “Covering Convex Sets with Non-Overlapping Polygons.” <i>Discrete Mathematics</i>, vol. 81, no. 2, Elsevier, 1990, pp. 153–64, doi:<a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">10.1016/0012-365X(90)90147-A</a>.","short":"H. Edelsbrunner, A. Robison, X. Shen, Discrete Mathematics 81 (1990) 153–164.","ama":"Edelsbrunner H, Robison A, Shen X. Covering convex sets with non-overlapping polygons. <i>Discrete Mathematics</i>. 1990;81(2):153-164. doi:<a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">10.1016/0012-365X(90)90147-A</a>","apa":"Edelsbrunner, H., Robison, A., &#38; Shen, X. (1990). Covering convex sets with non-overlapping polygons. <i>Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">https://doi.org/10.1016/0012-365X(90)90147-A</a>"},"doi":"10.1016/0012-365X(90)90147-A","language":[{"iso":"eng"}],"acknowledgement":"The first author acknowledges the support by Amoco Fnd. Fat. Dev. Comput. Sci. l-6-44862. Work on this paper by the second author was supported by a Shell Fellowship in Computer Science. The third author as supported by the office of Naval Research under grant NOOO14-86K-0416. ","date_created":"2018-12-11T12:06:44Z","extern":"1","month":"04","page":"153 - 164","intvolume":"        81","status":"public","quality_controlled":"1","publication":"Discrete Mathematics","publisher":"Elsevier"},{"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_updated":"2022-02-01T12:44:50Z","publication_identifier":{"issn":["0012-365X"],"eissn":["1872-681X"]},"article_type":"original","publist_id":"2019","oa_version":"None","year":"1986","volume":60,"publication_status":"published","_id":"4107","abstract":[{"lang":"eng","text":"A set of m planes dissects E3 into cells, facets, edges and vertices. Letting deg(c) be the number of facets that bound a cellc, we give exact and asymptotic bounds on the maximum of ∈cinCdeg(c), if C is a family of cells of the arrangement with fixed cardinality."}],"date_published":"1986-06-01T00:00:00Z","article_processing_charge":"No","issue":"C","language":[{"iso":"eng"}],"doi":"10.1016/0012-365X(86)90008-7","acknowledgement":"Research reported in the paper was conducted while the second author was visiting the Technical University of Graz. Support provided by the Technical University for this visit is gratefully acknowledged. ","day":"01","type":"journal_article","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"last_name":"Haussler","first_name":"David","full_name":"Haussler, David"}],"citation":{"mla":"Edelsbrunner, Herbert, and David Haussler. “The Complexity of Cells in 3-Dimensional Arrangements.” <i>Discrete Mathematics</i>, vol. 60, no. C, Elsevier, 1986, pp. 139–46, doi:<a href=\"https://doi.org/10.1016/0012-365X(86)90008-7\">10.1016/0012-365X(86)90008-7</a>.","chicago":"Edelsbrunner, Herbert, and David Haussler. “The Complexity of Cells in 3-Dimensional Arrangements.” <i>Discrete Mathematics</i>. Elsevier, 1986. <a href=\"https://doi.org/10.1016/0012-365X(86)90008-7\">https://doi.org/10.1016/0012-365X(86)90008-7</a>.","ieee":"H. Edelsbrunner and D. Haussler, “The complexity of cells in 3-dimensional arrangements,” <i>Discrete Mathematics</i>, vol. 60, no. C. Elsevier, pp. 139–146, 1986.","ista":"Edelsbrunner H, Haussler D. 1986. The complexity of cells in 3-dimensional arrangements. Discrete Mathematics. 60(C), 139–146.","ama":"Edelsbrunner H, Haussler D. The complexity of cells in 3-dimensional arrangements. <i>Discrete Mathematics</i>. 1986;60(C):139-146. doi:<a href=\"https://doi.org/10.1016/0012-365X(86)90008-7\">10.1016/0012-365X(86)90008-7</a>","apa":"Edelsbrunner, H., &#38; Haussler, D. (1986). The complexity of cells in 3-dimensional arrangements. <i>Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/0012-365X(86)90008-7\">https://doi.org/10.1016/0012-365X(86)90008-7</a>","short":"H. Edelsbrunner, D. Haussler, Discrete Mathematics 60 (1986) 139–146."},"title":"The complexity of cells in 3-dimensional arrangements","publication":"Discrete Mathematics","quality_controlled":"1","status":"public","intvolume":"        60","publisher":"Elsevier","month":"06","extern":"1","date_created":"2018-12-11T12:06:59Z","page":"139 - 146"}]