{"id":"https://openalex.org/W2148713750","doi":"https://doi.org/10.37236/1708","title":"A Discontinuity in the Distribution of Fixed Point Sums","display_name":"A Discontinuity in the Distribution of Fixed Point Sums","publication_year":2003,"publication_date":"2003-04-23","ids":{"openalex":"https://openalex.org/W2148713750","doi":"https://doi.org/10.37236/1708","mag":"2148713750"},"language":"en","primary_location":{"id":"doi:10.37236/1708","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1708","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r15/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":false,"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,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r15/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006144915","display_name":"Edward A. Bender","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Edward A. Bender","raw_affiliation_strings":["Department of Mathematics University of California, San Diego La Jolla, CA 92091"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of California, San Diego La Jolla, CA 92091","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071772779","display_name":"E. Rodney Canfield","orcid":null},"institutions":[{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E. Rodney Canfield","raw_affiliation_strings":["Department of Computer Science University of Georgia Athens, GA 30602"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science University of Georgia Athens, GA 30602","institution_ids":["https://openalex.org/I165733156"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030381054","display_name":"L. Bruce Richmond","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"L. Bruce Richmond","raw_affiliation_strings":["Department of Combinatorics and Optimization University of Waterloo Waterloo, Ontario CANADA N2L 3G1"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization University of Waterloo Waterloo, Ontario CANADA N2L 3G1","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112203336","display_name":"Herbert S. Wilf","orcid":null},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Herbert S. Wilf","raw_affiliation_strings":["Department of Mathematics University of Pennsylvania Philadelphia, PA 19104-6395"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Pennsylvania Philadelphia, PA 19104-6395","institution_ids":["https://openalex.org/I79576946"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5006144915"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.2201005,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"10","issue":"1","first_page":null,"last_page":null},"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":0.9976000189781189,"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":0.9976000189781189,"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":0.9932000041007996,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9866999983787537,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.869350790977478},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.8565797805786133},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8081367015838623},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.7205566763877869},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.6487013101577759},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5218238234519958},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4753289520740509},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.42218682169914246},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38682180643081665},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10146722197532654}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.869350790977478},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.8565797805786133},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8081367015838623},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.7205566763877869},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.6487013101577759},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5218238234519958},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4753289520740509},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.42218682169914246},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38682180643081665},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10146722197532654},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/1708","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1708","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r15/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":false,"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,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.3.5058","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.5058","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_10/PDF/v10i1r15.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.5.1599","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.1599","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_10/PostScriptfiles/v10i1r15.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.6.9240","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.9240","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.ucsd.edu/~ebender/reprints/107.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.78.1147","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.78.1147","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.ucsd.edu/~ebender/reprints/107.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1708","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1708","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r15/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":false,"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,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2148713750.pdf","grobid_xml":"https://content.openalex.org/works/W2148713750.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W2047572897","https://openalex.org/W2094836222","https://openalex.org/W2167266655","https://openalex.org/W2242479605","https://openalex.org/W4205333027","https://openalex.org/W4233743347","https://openalex.org/W4291474784","https://openalex.org/W4300302225"],"related_works":["https://openalex.org/W3039499377","https://openalex.org/W162062087","https://openalex.org/W2085032340","https://openalex.org/W2026226327","https://openalex.org/W1989965977","https://openalex.org/W2056095867","https://openalex.org/W2232767080","https://openalex.org/W1756153455","https://openalex.org/W2373997809","https://openalex.org/W2181452467"],"abstract_inverted_index":{"The":[0],"quantity":[1],"$f(n,r)$,":[2],"defined":[3],"as":[4],"the":[5,10,25,35,56,79,82],"number":[6],"of":[7,9,27,38,52,59,71,78],"permutations":[8],"set":[11,90],"$[n]=\\{1,2,\\dots":[12],"n\\}$":[13],"whose":[14],"fixed":[15],"points":[16],"sum":[17],"to":[18,49],"$r$,":[19],"shows":[20],"a":[21,75],"sharp":[22],"discontinuity":[23,32],"in":[24,41,74],"neighborhood":[26],"$r=n$.":[28],"We":[29,45],"explain":[30],"this":[31],"and":[33,89],"study":[34],"possible":[36],"existence":[37],"other":[39,50],"discontinuities":[40],"$f(n,r)$":[42,63],"for":[43],"permutations.":[44],"generalize":[46],"our":[47],"results":[48],"families":[51],"structures":[53],"that":[54],"exhibit":[55],"same":[57],"kind":[58],"discontinuities,":[60],"by":[61,69],"studying":[62],"when":[64],"\"fixed":[65],"points\"":[66],"is":[67],"replaced":[68],"\"components":[70],"size":[72],"1\"":[73],"suitable":[76],"graph":[77],"structure.":[80],"Among":[81],"objects":[83],"considered":[84],"are":[85],"permutations,":[86],"all":[87],"functions":[88],"partitions.":[91]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
