{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T09:09:38Z","timestamp":1763543378232,"version":"3.45.0"},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2025,9,12]],"date-time":"2025-09-12T00:00:00Z","timestamp":1757635200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2025,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We present an explicit subset\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S096354832510014X_inline1.png\"\/>\n                        <jats:tex-math>$A\\subseteq \\mathbb{N} = \\{0,1,\\ldots \\}$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    such that\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S096354832510014X_inline2.png\"\/>\n                        <jats:tex-math>$A + A = \\mathbb{N}$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    and for all\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S096354832510014X_inline3.png\"\/>\n                        <jats:tex-math>$\\varepsilon \\gt 0$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    ,\n                    <jats:disp-formula>\n                      <jats:alternatives>\n                        <jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" position=\"float\" xlink:href=\"S096354832510014X_eqnU1.png\"\/>\n                        <jats:tex-math>\\begin{equation*}\\lim _{N\\to \\infty }\\frac {\\big |\\big \\{(n_1,n_2): n_1 + n_2 = N, (n_1,n_2)\\in A^2\\big \\}\\big |}{N^{\\varepsilon }} = 0.\\end{equation*}<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:disp-formula>\n                  <\/jats:p>\n                  <jats:p>This answers a question of Erd\u0151s.<\/jats:p>","DOI":"10.1017\/s096354832510014x","type":"journal-article","created":{"date-parts":[[2025,9,12]],"date-time":"2025-09-12T08:12:36Z","timestamp":1757664756000},"page":"815-820","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["An explicit economical additive basis"],"prefix":"10.1017","volume":"34","author":[{"given":"Vishesh","family":"Jain","sequence":"first","affiliation":[{"name":"University of Illinois Chicago"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huy Tuan","family":"Pham","sequence":"additional","affiliation":[{"name":"Stanford University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mehtaab","family":"Sawhney","sequence":"additional","affiliation":[{"name":"Columbia University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dmitrii","family":"Zakharov","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,9,12]]},"reference":[{"key":"S096354832510014X_ref8","first-page":"165","article-title":"Some of my favourite problems in number theory, combinatorics, and geometry","volume":"2","author":"Erd\u0151s","year":"1995","journal-title":"Combin. 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