{"id":"https://openalex.org/W2575096499","doi":"https://doi.org/10.1137/16m1099182","title":"Improved Bounds on Sidon Sets via Lattice Packings of Simplices","display_name":"Improved Bounds on Sidon Sets via Lattice Packings of Simplices","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2575096499","doi":"https://doi.org/10.1137/16m1099182","mag":"2575096499"},"language":"en","primary_location":{"id":"doi:10.1137/16m1099182","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1099182","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1610.01341","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Mladen Kova\u010devi\u0107","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mladen Kova\u010devi\u0107","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Vincent Y. F. Tan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vincent Y. F. Tan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.916,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82866618,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"31","issue":"3","first_page":"2269","last_page":"2278"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.18700000643730164,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.18700000643730164,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.07919999957084656,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.06469999998807907,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.7814000248908997},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6444000005722046},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5893999934196472},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4607999920845032},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4415000081062317},{"id":"https://openalex.org/keywords/elementary-abelian-group","display_name":"Elementary abelian group","score":0.36890000104904175},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.33239999413490295},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.33169999718666077}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8729000091552734},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7986000180244446},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7814000248908997},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6444000005722046},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5893999934196472},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4607999920845032},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4415000081062317},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4390000104904175},{"id":"https://openalex.org/C81008192","wikidata":"https://www.wikidata.org/wiki/Q1017231","display_name":"Elementary abelian group","level":3,"score":0.36890000104904175},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.33169999718666077},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C142885752","wikidata":"https://www.wikidata.org/wiki/Q1252145","display_name":"Integer lattice","level":3,"score":0.2976999878883362},{"id":"https://openalex.org/C183893376","wikidata":"https://www.wikidata.org/wiki/Q900117","display_name":"Sphere packing","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.2903999984264374},{"id":"https://openalex.org/C197623797","wikidata":"https://www.wikidata.org/wiki/Q1454111","display_name":"Free abelian group","level":5,"score":0.2831000089645386},{"id":"https://openalex.org/C188204562","wikidata":"https://www.wikidata.org/wiki/Q5275281","display_name":"Difference set","level":3,"score":0.28110000491142273},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.27140000462532043},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.26460000872612},{"id":"https://openalex.org/C156491182","wikidata":"https://www.wikidata.org/wiki/Q752723","display_name":"Natural density","level":2,"score":0.258899986743927}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1099182","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1099182","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1610.01341","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.01341","pdf_url":"https://arxiv.org/pdf/1610.01341","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1610.01341","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.01341","pdf_url":"https://arxiv.org/pdf/1610.01341","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3077877989","display_name":null,"funder_award_id":"R-263-000-B61-112","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1892868620","https://openalex.org/W1965994418","https://openalex.org/W1977565656","https://openalex.org/W2009888012","https://openalex.org/W2023105174","https://openalex.org/W2030243808","https://openalex.org/W2033489004","https://openalex.org/W2034430120","https://openalex.org/W2067495494","https://openalex.org/W2070938277"],"related_works":[],"abstract_inverted_index":{"A":[0],"$":[1,3,10,17,19,23,27,29,31,39,45,56,58,69,71,75,98,101,109,137,139,152,154],"B_h":[2,70],"set":[4,7,72],"(or":[5],"Sidon":[6],"of":[8,28,52,62,73,107,148,150,161],"order":[9,51,61,151],"h":[11,153],"$)":[12,131],"in":[13,112,120,140,155,159],"an":[14,108],"Abelian":[15,65,157],"group":[16,66],"G":[18,30],"is":[20,81,102,125,166],"any":[21],"subset":[22],"\\{b_0,":[24],"b_1,":[25],"\\ldots,b_{n}\\}":[26],"with":[32],"the":[33,37,50,53,60,63,103,117,141],"property":[34],"that":[35,83],"all":[36],"sums":[38],"b_{i_1}":[40],"+":[41,43,77],"\\cdots":[42],"b_{i_h}":[44],"are":[46],"different":[47],"up":[48],"to":[49],"summands.":[54],"Let":[55],"\\phi(h,n)":[57,88,138],"denote":[59],"smallest":[64],"containing":[67],"a":[68],"cardinality":[74],"n":[76,110,128],"1":[78],"$.":[79],"It":[80],"shown":[82],"${\\scriptstyle\\lim_{h":[84],"\\to":[85],"\\infty}":[86],"\\frac{":[87],"}{":[89],"h^n":[90],"}":[91],"=":[92],"\\frac{1}{n!":[93],"\\":[94],"\\delta_{\\sc":[95,99],"l}(\\triangle^n)}},$":[96],"where":[97,122],"l}(\\triangle^n)":[100],"lattice":[104,162],"packing":[105],"density":[106,124],"$-simplex":[111],"Euclidean":[113],"space.":[114],"This":[115],"determines":[116],"asymptotics":[118],"exactly":[119],"cases":[121],"this":[123],"known":[126],"($":[127],"\\leq":[129],"3":[130],"and":[132],"gives":[133],"improved":[134],"bounds":[135],"on":[136],"remaining":[142],"cases.":[143],"The":[144],"corresponding":[145],"geometric":[146],"characterization":[147],"bases":[149],"finite":[156],"groups":[158],"terms":[160],"coverings":[163],"by":[164],"simplices":[165],"also":[167],"given.":[168]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2017-01-26T00:00:00"}