{"id":"https://openalex.org/W2095642300","doi":"https://doi.org/10.37236/651","title":"Isoperimetric Numbers of Regular Graphs of High Degree with Applications to Arithmetic Riemann Surfaces","display_name":"Isoperimetric Numbers of Regular Graphs of High Degree with Applications to Arithmetic Riemann Surfaces","publication_year":2011,"publication_date":"2011-08-12","ids":{"openalex":"https://openalex.org/W2095642300","doi":"https://doi.org/10.37236/651","mag":"2095642300"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.37236/651","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p164/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p164/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083593533","display_name":"Dominic Lanphier","orcid":"https://orcid.org/0000-0002-2378-5416"},"institutions":[{"id":"https://openalex.org/I94339441","display_name":"Western Kentucky University","ror":"https://ror.org/0446vnd56","country_code":"US","type":"education","lineage":["https://openalex.org/I94339441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dominic Lanphier","raw_affiliation_strings":["Western Kentucky University,"],"affiliations":[{"raw_affiliation_string":"Western Kentucky University,","institution_ids":["https://openalex.org/I94339441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077629661","display_name":"Jason Rosenhouse","orcid":null},"institutions":[{"id":"https://openalex.org/I11883440","display_name":"James Madison University","ror":"https://ror.org/028pmsz77","country_code":"US","type":"education","lineage":["https://openalex.org/I11883440"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jason Rosenhouse","raw_affiliation_strings":["JAMES MADISON UNIVERSITY"],"affiliations":[{"raw_affiliation_string":"JAMES MADISON UNIVERSITY","institution_ids":["https://openalex.org/I11883440"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":0,"currency":"USD","value_usd":0,"provenance":"doaj"},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":1,"citation_normalized_percentile":{"value":0.308179,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":65,"max":72},"biblio":{"volume":"18","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9993,"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"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9992,"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/degree","display_name":"Degree (music)","score":0.73169637},{"id":"https://openalex.org/keywords/asymptotic-formula","display_name":"Asymptotic formula","score":0.46154597}],"concepts":[{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.9052621},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.891328},{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.7788613},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.73517364},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.73169637},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.46764705},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.46154597},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4581368},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.44677332},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.44652182},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40965363},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16484311},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12540543},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.37236/651","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p164/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.37236/651","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p164/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":19,"referenced_works":["https://openalex.org/W1512234150","https://openalex.org/W1512248353","https://openalex.org/W1530740238","https://openalex.org/W1993216347","https://openalex.org/W1995003453","https://openalex.org/W2003791246","https://openalex.org/W2008865083","https://openalex.org/W2025194025","https://openalex.org/W2027199101","https://openalex.org/W2032686120","https://openalex.org/W2034316495","https://openalex.org/W2045377861","https://openalex.org/W2057146791","https://openalex.org/W2132317856","https://openalex.org/W2132890668","https://openalex.org/W2166435158","https://openalex.org/W2986001730","https://openalex.org/W4299787127","https://openalex.org/W594938858"],"related_works":["https://openalex.org/W4327810916","https://openalex.org/W4302315593","https://openalex.org/W4302283109","https://openalex.org/W2995636218","https://openalex.org/W2903611028","https://openalex.org/W2758778865","https://openalex.org/W2463024015","https://openalex.org/W2043332011","https://openalex.org/W1967915210","https://openalex.org/W1701336714"],"abstract_inverted_index":{"We":[0,37,82],"derive":[1],"upper":[2],"and":[3,10,27,48,71],"lower":[4],"bounds":[5,40,77,86,103],"on":[6,87],"the":[7,34,49,53,57,79,88,108],"isoperimetric":[8,80],"numbers":[9],"bisection":[11],"widths":[12],"of":[13,17,20,33,45,91,99],"a":[14,31,96],"large":[15,97],"class":[16,98],"regular":[18,43],"graphs":[19,44,51,64],"high":[21,46],"degree.":[22],"Our":[23],"methods":[24],"are":[25,65,104],"combinatorial":[26],"do":[28],"not":[29],"require":[30],"knowledge":[32],"eigenvalue":[35],"spectrum.":[36],"apply":[38],"these":[39,63,100,102],"to":[41],"random":[42],"degree":[47],"Platonic":[50],"over":[52,107],"rings":[54],"$\\mathbb{Z}_n$.":[55],"In":[56],"latter":[58],"case":[59],"we":[60,72],"show":[61],"that":[62],"generally":[66],"non-Ramanujan":[67],"for":[68,78],"composite":[69],"$n$":[70],"also":[73],"give":[74],"sharp":[75],"asymptotic":[76,110],"numbers.":[81],"conclude":[83],"by":[84],"giving":[85],"Cheeger":[89],"constants":[90],"arithmetic":[92],"Riemann":[93],"surfaces.":[94],"For":[95],"surfaces":[101],"an":[105],"improvement":[106],"known":[109],"bounds.":[111]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2095642300","counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2024-12-11T14:17:21.273782","created_date":"2016-06-24"}