{"id":"https://openalex.org/W3186461226","doi":"https://doi.org/10.1007/s00493-023-00008-9","title":"A combinatorial proof of a sumset conjecture of Furstenberg","display_name":"A combinatorial proof of a sumset conjecture of Furstenberg","publication_year":2023,"publication_date":"2023-04-01","ids":{"openalex":"https://openalex.org/W3186461226","doi":"https://doi.org/10.1007/s00493-023-00008-9","mag":"3186461226"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-023-00008-9","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00493-023-00008-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-023-00008-9.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00493-023-00008-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015438673","display_name":"Daniel Glasscock","orcid":null},"institutions":[{"id":"https://openalex.org/I133738476","display_name":"University of Massachusetts Lowell","ror":"https://ror.org/03hamhx47","country_code":"US","type":"education","lineage":["https://openalex.org/I133738476"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Glasscock","raw_affiliation_strings":["University of Massachusetts Lowell, Lowell, USA"],"affiliations":[{"raw_affiliation_string":"University of Massachusetts Lowell, Lowell, USA","institution_ids":["https://openalex.org/I133738476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085306379","display_name":"Joel Moreira","orcid":"https://orcid.org/0000-0002-7278-1219"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Joel Moreira","raw_affiliation_strings":["University of Warwick, Coventry, UK"],"affiliations":[{"raw_affiliation_string":"University of Warwick, Coventry, UK","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109420647","display_name":"Florian K. Richter","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Florian K. Richter","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109420647"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":0.5412,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48800246,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"43","issue":"2","first_page":"299","last_page":"328"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9854000210762024,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9761000275611877,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/algorithm","display_name":"Algorithm","score":0.5276266932487488},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28272736072540283}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5276266932487488},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28272736072540283}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00493-023-00008-9","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00493-023-00008-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-023-00008-9.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2107.10605","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2107.10605","pdf_url":"https://arxiv.org/pdf/2107.10605","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"},{"id":"pmh:oai:wrap.warwick.ac.uk:163724","is_oa":true,"landing_page_url":"https://wrap.warwick.ac.uk/163724/1/WRAP-combinatorial-proof-sumset-conjecture-Furstenberg-Moreira-2022.pdf","pdf_url":"https://wrap.warwick.ac.uk/163724/7/WRAP-combinatorial-proof-sumset-conjecture-Furstenberg-Moreira-2022.pdf","source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:infoscience.epfl.ch:290211","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/290211","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"research article"}],"best_oa_location":{"id":"doi:10.1007/s00493-023-00008-9","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00493-023-00008-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-023-00008-9.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3186461226.pdf"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W43370847","https://openalex.org/W1504907986","https://openalex.org/W1513934683","https://openalex.org/W1607458528","https://openalex.org/W1655809325","https://openalex.org/W2059735611","https://openalex.org/W2087241155","https://openalex.org/W2113591200","https://openalex.org/W2114357685","https://openalex.org/W2115798948","https://openalex.org/W2120045167","https://openalex.org/W2152491771","https://openalex.org/W2157752343","https://openalex.org/W2301497234","https://openalex.org/W2321667127","https://openalex.org/W2515980152","https://openalex.org/W2943612991","https://openalex.org/W2962754787","https://openalex.org/W2963687316","https://openalex.org/W2963740364","https://openalex.org/W2964089240","https://openalex.org/W3022983756","https://openalex.org/W3082053321","https://openalex.org/W3102741732","https://openalex.org/W3105879936","https://openalex.org/W3105949937","https://openalex.org/W3134007037","https://openalex.org/W3135377600","https://openalex.org/W3186276178","https://openalex.org/W4205356037","https://openalex.org/W4240810995","https://openalex.org/W4302394292"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2544423928","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2052122378","https://openalex.org/W2989452537","https://openalex.org/W4313731559"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"give":[2],"a":[3,7,151,176,183],"new":[4],"proof":[5,160],"of":[6,10,65,131,154,167,190],"sumset":[8,133],"conjecture":[9],"Furstenberg":[11],"that":[12,187],"was":[13],"first":[14],"proved":[15],"by":[16],"Hochman":[17],"and":[18,38,40,53,163,171,182],"Shmerkin":[19],"in":[20],"2012:":[21],"if":[22],"$$\\log":[23],"r/\\log":[24],"s$$":[25,55],"<mml:math":[26,45,56,87,139],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[27,46,57,88,140],"<mml:mrow>":[28,47,58,89,94,103,141],"<mml:mo>log</mml:mo>":[29,32],"<mml:mi>r</mml:mi>":[30,49],"<mml:mo>/</mml:mo>":[31],"<mml:mi>s</mml:mi>":[33,60],"</mml:mrow>":[34,50,61,100,119,120,147],"</mml:math>":[35,51,62,121,148],"is":[36,161],"irrational":[37],"X":[39,135],"Y":[41,74],"are":[42],"$$\\times":[43,54],"r$$":[44],"<mml:mo>\u00d7</mml:mo>":[48,59],"-":[52],"-invariant":[63],"subsets":[64],"[0,":[66],"1],":[67],"respectively,":[68],"then":[69],"$$\\dim":[70],"_{\\text":[71,80,84],"{H}}(X":[72],"+":[73,82,136],")":[75],"=":[76],"\\min":[77],"(1,":[78],"\\dim":[79,83],"{H}}X":[81],"{H}}Y":[85],")$$":[86],"<mml:msub>":[90,107,113],"<mml:mo>dim</mml:mo>":[91,108,114],"<mml:mtext>H</mml:mtext>":[92,109,115],"</mml:msub>":[93,110,116],"<mml:mo>(</mml:mo>":[95,104],"<mml:mi>X</mml:mi>":[96,111,143],"<mml:mo>+</mml:mo>":[97,112,144],"<mml:mi>Y</mml:mi>":[98,117,146],"<mml:mo>)</mml:mo>":[99,118],"<mml:mo>=</mml:mo>":[101],"<mml:mo>min</mml:mo>":[102],"<mml:mn>1</mml:mn>":[105],"<mml:mo>,</mml:mo>":[106],".":[122],"Our":[123],"main":[124],"result":[125],"yields":[126],"information":[127],"on":[128,175],"the":[129,132,165],"size":[130],"$$\\lambda":[134],"\\eta":[137],"Y$$":[138],"<mml:mi>\u03bb</mml:mi>":[142],"<mml:mi>\u03b7</mml:mi>":[145],"uniformly":[149],"across":[150],"compact":[152],"set":[153],"parameters":[155],"at":[156],"fixed":[157],"scales.":[158],"The":[159],"combinatorial":[162],"avoids":[164],"machinery":[166],"local":[168],"entropy":[169],"averages":[170],"CP-processes,":[172],"relying":[173],"instead":[174],"quantitative,":[177],"discrete":[178],"Marstrand":[179],"projection":[180],"theorem":[181,186],"subtree":[184],"regularity":[185],"may":[188],"be":[189],"independent":[191],"interest.":[192]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}