{"id":"https://openalex.org/W7163261166","doi":"https://doi.org/10.48550/arxiv.2606.00996","title":"On Rounding on the Hypersimplex","display_name":"On Rounding on the Hypersimplex","publication_year":2026,"publication_date":"2026-05-31","ids":{"openalex":"https://openalex.org/W7163261166","doi":"https://doi.org/10.48550/arxiv.2606.00996"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.00996","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.00996","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.00996","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040375566","display_name":"Nima Anari","orcid":"https://orcid.org/0000-0002-4394-3530"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Anari, Nima","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137618061","display_name":"Alireza Haqi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haqi, Alireza","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5048865749","display_name":"Eric Ma","orcid":"https://orcid.org/0000-0003-0041-5989"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ma, Eric","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":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.41780000925064087,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.41780000925064087,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.33379998803138733,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0625,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.8986999988555908},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.5135999917984009},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.47450000047683716},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.4625999927520752},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.460099995136261},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.40149998664855957},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.375900000333786}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.8986999988555908},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6614999771118164},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.621999979019165},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.5135999917984009},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5034000277519226},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.47450000047683716},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.4625999927520752},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.460099995136261},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.40149998664855957},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3822000026702881},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.375900000333786},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.35830000042915344},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3294000029563904},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.3246999979019165},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.31839999556541443},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2915000021457672},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2903999984264374},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2865999937057495},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C100279318","wikidata":"https://www.wikidata.org/wiki/Q467440","display_name":"Sample space","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.00996","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.00996","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.00996","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.00996","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,48],"study":[1],"correlated":[2,133],"rounding":[3,134],"on":[4,60,122],"the":[5,7,11,19,21,34,54,66,70,85,88,123,126,141,162,172],"hypersimplex,":[6,20],"base":[8],"polytope":[9],"of":[10,39,65,69],"uniform":[12,102],"matroid.":[13],"For":[14,104],"each":[15],"point":[16],"\\(x\\)":[17,40],"in":[18],"goal":[22],"is":[23],"to":[24,137],"sample":[25],"a":[26,61,96,138,155],"\\(k\\)-subset":[27,90],"\\(A(x)\\)":[28],"with":[29,92,107],"marginals":[30,94],"\\(x\\),":[31],"while":[32],"coupling":[33],"samples":[35,87],"for":[36,53,131,171],"all":[37],"choices":[38],"so":[41],"that":[42],"nearby":[43,46],"inputs":[44],"produce":[45],"sets.":[47],"give":[49],"conditional":[50,121,164],"constant-stretch":[51],"results":[52],"natural":[55],"maximum-entropy":[56,71,89],"sequential":[57],"scheme,":[58],"based":[59],"conjectured":[62],"spectral":[63,124],"property":[64],"covariance":[67],"matrix":[68],"distribution":[72,91],"over":[73],"\\(k\\)-subsets;":[74],"this":[75,83],"conjecture":[76],"has":[77],"been":[78],"extensively":[79],"tested":[80],"numerically.":[81],"Under":[82],"property,":[84],"scheme":[86],"prescribed":[93],"using":[95],"common":[97,101],"random":[98],"ordering":[99],"and":[100,140,151],"thresholds.":[103],"every":[105],"\\(x,y\\in[0,1]^n\\)":[106],"\\(\\sum_i":[108],"x_i=\\sum_i":[109],"y_i=k\\),":[110],"it":[111],"satisfies":[112],"\\[":[113],"\\mathbb{E}\\!\\left[|A(x)\\triangle":[114],"A(y)|\\right]":[115],"\\le":[116],"6\\|x-y\\|_1":[117],".":[118],"\\]":[119],"Thus,":[120],"hypothesis,":[125],"previous":[127],"\\(O(\\log":[128],"k)\\)":[129],"bound":[130],"hypersimplex":[132],"would":[135,153],"improve":[136],"constant":[139],"open":[142],"question":[143],"raised":[144],"by":[145],"Naor,":[146],"Raju,":[147],"Shetty,":[148],"Srinivasan,":[149],"Valieva,":[150],"Wajc":[152],"have":[154],"positive":[156],"answer.":[157],"By":[158],"adding":[159],"dummy":[160],"coordinates,":[161],"same":[163],"result":[165],"gives":[166],"stretch":[167],"at":[168],"most":[169],"\\(12\\)":[170],"at-most-\\(k\\)":[173],"polytope.":[174]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-03T00:00:00"}
