[{"corr_author":"1","page":"1059-1156","external_id":{"isi":["001366233800004"],"arxiv":["2201.04554"]},"fulldoi":"https://doi.org/10.4007/annals.2024.200.3.4","citation":{"ama":"Kwan MA, Sah A, Sawhney M, Simkin M. High-girth Steiner triple systems. <i>Annals of Mathematics</i>. 2024;200(3):1059-1156. doi:<a href=\"https://doi.org/10.4007/annals.2024.200.3.4\">10.4007/annals.2024.200.3.4</a>","apa":"Kwan, M. A., Sah, A., Sawhney, M., &#38; Simkin, M. (2024). High-girth Steiner triple systems. <i>Annals of Mathematics</i>. Princeton University. <a href=\"https://doi.org/10.4007/annals.2024.200.3.4\">https://doi.org/10.4007/annals.2024.200.3.4</a>","ista":"Kwan MA, Sah A, Sawhney M, Simkin M. 2024. High-girth Steiner triple systems. Annals of Mathematics. 200(3), 1059–1156.","ieee":"M. A. Kwan, A. Sah, M. Sawhney, and M. Simkin, “High-girth Steiner triple systems,” <i>Annals of Mathematics</i>, vol. 200, no. 3. Princeton University, pp. 1059–1156, 2024.","mla":"Kwan, Matthew Alan, et al. “High-Girth Steiner Triple Systems.” <i>Annals of Mathematics</i>, vol. 200, no. 3, Princeton University, 2024, pp. 1059–156, doi:<a href=\"https://doi.org/10.4007/annals.2024.200.3.4\">10.4007/annals.2024.200.3.4</a>.","short":"M.A. Kwan, A. Sah, M. Sawhney, M. Simkin, Annals of Mathematics 200 (2024) 1059–1156.","chicago":"Kwan, Matthew Alan, Ashwin Sah, Mehtaab Sawhney, and Michael Simkin. “High-Girth Steiner Triple Systems.” <i>Annals of Mathematics</i>. Princeton University, 2024. <a href=\"https://doi.org/10.4007/annals.2024.200.3.4\">https://doi.org/10.4007/annals.2024.200.3.4</a>."},"isi":1,"article_type":"original","intvolume":"       200","date_created":"2024-11-17T23:01:48Z","publisher":"Princeton University","researchdata_availability":"no","date_updated":"2026-10-16T10:12:22Z","language":[{"iso":"eng"}],"department":[{"_id":"MaKw"}],"author":[{"last_name":"Kwan","full_name":"Kwan, Matthew Alan","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3"},{"last_name":"Sah","first_name":"Ashwin","full_name":"Sah, Ashwin"},{"last_name":"Sawhney","first_name":"Mehtaab","full_name":"Sawhney, Mehtaab"},{"last_name":"Simkin","full_name":"Simkin, Michael","first_name":"Michael"}],"oa":1,"arxiv":1,"abstract":[{"text":"We prove a 1973 conjecture due to Erdős on the existence of Steiner triple systems with arbitrarily high girth.","lang":"eng"}],"oa_version":"Preprint","das_tickbox":"0","day":"01","doi":"10.4007/annals.2024.200.3.4","volume":200,"publication":"Annals of Mathematics","issue":"3","quality_controlled":"1","month":"11","publication_identifier":{"eissn":["1939-8980"],"issn":["0003-486X"]},"article_processing_charge":"No","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","supplementarymaterial":"yes","status":"public","type":"journal_article","acknowledgement":"Sah and Sawhney were supported by NSF Graduate Research Fellowship Program DGE1745302. Sah was supported by the PD Soros Fellowship. Simkin was supported by the Center of Mathematical Sciences and Applications at Harvard University.","date_published":"2024-11-01T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2201.04554","open_access":"1"}],"year":"2024","_id":"18559","OA_place":"repository","title":"High-girth Steiner triple systems","scopus_import":"1","OA_type":"green"},{"article_type":"original","intvolume":"       158","page":"1067 - 1080","external_id":{"arxiv":["0205088"]},"fulldoi":"https://doi.org/10.4007/annals.2003.158.1067 ","citation":{"ama":"Lieb É, Seiringer R, Yngvason J. Poincaré inequalities in punctured domains. <i>Annals of Mathematics</i>. 2003;158(3):1067-1080. doi:<a href=\"https://doi.org/10.4007/annals.2003.158.1067 \">10.4007/annals.2003.158.1067 </a>","apa":"Lieb, É., Seiringer, R., &#38; Yngvason, J. (2003). Poincaré inequalities in punctured domains. <i>Annals of Mathematics</i>. Princeton University Press. <a href=\"https://doi.org/10.4007/annals.2003.158.1067 \">https://doi.org/10.4007/annals.2003.158.1067 </a>","ista":"Lieb É, Seiringer R, Yngvason J. 2003. Poincaré inequalities in punctured domains. Annals of Mathematics. 158(3), 1067–1080.","ieee":"É. Lieb, R. Seiringer, and J. Yngvason, “Poincaré inequalities in punctured domains,” <i>Annals of Mathematics</i>, vol. 158, no. 3. Princeton University Press, pp. 1067–1080, 2003.","mla":"Lieb, Élliott, et al. “Poincaré Inequalities in Punctured Domains.” <i>Annals of Mathematics</i>, vol. 158, no. 3, Princeton University Press, 2003, pp. 1067–80, doi:<a href=\"https://doi.org/10.4007/annals.2003.158.1067 \">10.4007/annals.2003.158.1067 </a>.","short":"É. Lieb, R. Seiringer, J. Yngvason, Annals of Mathematics 158 (2003) 1067–1080.","chicago":"Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “Poincaré Inequalities in Punctured Domains.” <i>Annals of Mathematics</i>. Princeton University Press, 2003. <a href=\"https://doi.org/10.4007/annals.2003.158.1067 \">https://doi.org/10.4007/annals.2003.158.1067 </a>."},"date_created":"2018-12-11T11:57:11Z","publisher":"Princeton University Press","language":[{"iso":"eng"}],"date_updated":"2026-05-28T08:25:42Z","oa":1,"arxiv":1,"author":[{"first_name":"Élliott","full_name":"Lieb, Élliott","last_name":"Lieb"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"},{"last_name":"Yngvason","full_name":"Yngvason, Jakob","first_name":"Jakob"}],"day":"01","doi":"10.4007/annals.2003.158.1067 ","publication":"Annals of Mathematics","volume":158,"issue":"3","abstract":[{"text":"The classic Poincaré inequality bounds the L q-norm of a function f in a bounded domain Ω ⊂ ℝ n in terms of some L p-norm of its gradient in Ω. We generalize this in two ways: In the first generalization we remove a set Τ from Ω and concentrate our attention on Λ = Ω \\ Τ. This new domain might not even be connected and hence no Poincaré inequality can generally hold for it, or if it does hold it might have a very bad constant. This is so even if the volume of Τ is arbitrarily small. A Poincaré inequality does hold, however, if one makes the additional assumption that f has a finite L p gradient norm on the whole of Ω, not just on Λ. The important point is that the Poincaré inequality thus obtained bounds the L q-norm of f in terms of the L p gradient norm on Λ (not Ω) plus an additional term that goes to zero as the volume of Τ goes to zero. This error term depends on Τ only through its volume. Apart from this additive error term, the constant in the inequality remains that of the 'nice' domain Ω. In the second generalization we are given a vector field A and replace ∇ by ∇ + iA(x) (geometrically, a connection on a U(1) bundle). Unlike the A = 0 case, the infimum of ∥(∇ + iA)f∥ p over all f with a given ∥f∥ q is in general not zero. This permits an improvement of the inequality by the addition of a term whose sharp value we derive. We describe some open problems that arise from these generalizations.","lang":"eng"}],"publist_id":"4570","oa_version":"Published Version","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","extern":"1","publication_status":"published","quality_controlled":"1","month":"11","publication_identifier":{"eissn":["1939-8980"],"issn":["0003-486X"]},"article_processing_charge":"No","main_file_link":[{"url":"http://arxiv.org/abs/math/0205088","open_access":"1"}],"year":"2003","_id":"2357","status":"public","type":"journal_article","date_published":"2003-11-01T00:00:00Z","OA_type":"free access","OA_place":"publisher","title":"Poincaré inequalities in punctured domains","scopus_import":"1"}]