{"publist_id":"6996","has_accepted_license":"1","date_updated":"2021-01-12T08:11:28Z","publication_status":"published","language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:47:47Z","file":[{"creator":"system","file_name":"IST-2018-984-v1+1_Patakova_on_the_nonexistence_of_k-reptile_simplices_in_R_3_and_R_4_2017.pdf","content_type":"application/pdf","file_size":544042,"access_level":"open_access","date_updated":"2020-07-14T12:47:47Z","file_id":"5077","relation":"main_file","date_created":"2018-12-12T10:14:25Z","checksum":"a431e573e31df13bc0f66de3061006ec"}],"month":"07","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"14","_id":"701","page":"1-44","type":"journal_article","publication":"The Electronic Journal of Combinatorics","volume":24,"citation":{"ista":"Kynčl J, Patakova Z. 2017. On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4. The Electronic Journal of Combinatorics. 24(3), 1–44.","ama":"Kynčl J, Patakova Z. On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4. <i>The Electronic Journal of Combinatorics</i>. 2017;24(3):1-44.","mla":"Kynčl, Jan, and Zuzana Patakova. “On the Nonexistence of k Reptile Simplices in ℝ^3 and ℝ^4.” <i>The Electronic Journal of Combinatorics</i>, vol. 24, no. 3, International Press, 2017, pp. 1–44.","chicago":"Kynčl, Jan, and Zuzana Patakova. “On the Nonexistence of k Reptile Simplices in ℝ^3 and ℝ^4.” <i>The Electronic Journal of Combinatorics</i>. International Press, 2017.","short":"J. Kynčl, Z. Patakova, The Electronic Journal of Combinatorics 24 (2017) 1–44.","ieee":"J. Kynčl and Z. Patakova, “On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4,” <i>The Electronic Journal of Combinatorics</i>, vol. 24, no. 3. International Press, pp. 1–44, 2017.","apa":"Kynčl, J., &#38; Patakova, Z. (2017). On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4. <i>The Electronic Journal of Combinatorics</i>. International Press."},"date_published":"2017-07-14T00:00:00Z","pubrep_id":"984","year":"2017","ddc":["500"],"issue":"3","status":"public","oa_version":"Submitted Version","title":"On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4","department":[{"_id":"UlWa"}],"intvolume":"        24","publisher":"International Press","author":[{"last_name":"Kynčl","full_name":"Kynčl, Jan","first_name":"Jan"},{"full_name":"Patakova, Zuzana","orcid":"0000-0002-3975-1683","last_name":"Patakova","first_name":"Zuzana","id":"48B57058-F248-11E8-B48F-1D18A9856A87"}],"abstract":[{"lang":"eng","text":"A d-dimensional simplex S is called a k-reptile (or a k-reptile simplex) if it can be tiled by k simplices with disjoint interiors that are all mutually congruent and similar to S. For d = 2, triangular k-reptiles exist for all k of the form a^2, 3a^2 or a^2+b^2 and they have been completely characterized by Snover, Waiveris, and Williams. On the other hand, the only k-reptile simplices that are known for d ≥ 3, have k = m^d, where m is a positive integer. We substantially simplify the proof by Matoušek and the second author that for d = 3, k-reptile tetrahedra can exist only for k = m^3. We then prove a weaker analogue of this result for d = 4 by showing that four-dimensional k-reptile simplices can exist only for k = m^2."}],"oa":1,"date_created":"2018-12-11T11:48:00Z","publication_identifier":{"issn":["10778926"]}}