{"id":"https://openalex.org/W2096956500","doi":"https://doi.org/10.37236/1733","title":"Asymptotics of Permutations with Nearly Periodic Patterns of Rises and Falls","display_name":"Asymptotics of Permutations with Nearly Periodic Patterns of Rises and Falls","publication_year":2003,"publication_date":"2003-10-23","ids":{"openalex":"https://openalex.org/W2096956500","doi":"https://doi.org/10.37236/1733","mag":"2096956500"},"language":"en","primary_location":{"id":"doi:10.37236/1733","is_oa":false,"landing_page_url":"https://doi.org/10.37236/1733","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006144915","display_name":"Edward A. Bender","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Edward A. Bender","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036385461","display_name":"William Helton","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"William J. Helton","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5030381054","display_name":"L. Bruce Richmond","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. Bruce Richmond","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5006144915"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.20190859,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9991999864578247,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9991999864578247,"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":0.9977999925613403,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9977999925613403,"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/mathematics","display_name":"Mathematics","score":0.8952261805534363},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.8047443628311157},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7940119504928589},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6325249075889587},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5168972015380859},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24026241898536682},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05120667815208435}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8952261805534363},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.8047443628311157},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7940119504928589},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6325249075889587},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5168972015380859},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24026241898536682},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05120667815208435},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1733","is_oa":false,"landing_page_url":"https://doi.org/10.37236/1733","pdf_url":null,"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:10.1.1.9.5417","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.9.5417","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/v10i1r40.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1555674425","https://openalex.org/W2022806724","https://openalex.org/W2055226795","https://openalex.org/W2060304936","https://openalex.org/W2086449672","https://openalex.org/W2150654349","https://openalex.org/W2156810229"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W4302778552"],"abstract_inverted_index":{"Ehrenborg":[0],"obtained":[1],"asymptotic":[2,11,37],"results":[3],"for":[4,13,71],"nearly":[5,21],"alternating":[6],"permutations":[7,17,40],"and":[8,50],"conjectured":[9],"an":[10,68],"formula":[12],"the":[14,33,36,47,55,81],"number":[15,38],"of":[16,29,39,62],"that":[18,35],"have":[19],"a":[20,27,42,72],"periodic":[22,43],"run":[23,44],"pattern.":[24],"We":[25],"prove":[26],"generalization":[28],"this":[30],"conjecture,":[31],"rederive":[32],"fact":[34],"with":[41],"pattern":[45],"has":[46],"form":[48],"$Cr^{-n}\\,n!$,":[49],"show":[51],"how":[52],"to":[53,67],"compute":[54],"various":[56],"constants.":[57],"A":[58],"reformulation":[59],"in":[60],"terms":[61],"iid":[63],"random":[64],"variables":[65],"leads":[66],"eigenvalue":[69],"problem":[70],"Fredholm":[73],"integral":[74],"equation.":[75],"Tools":[76],"from":[77],"functional":[78],"analysis":[79],"establish":[80],"necessary":[82],"properties.":[83]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}