{"id":"https://openalex.org/W1981225400","doi":"https://doi.org/10.1017/s0963548306007905","title":"The Application of Non-Crossing Partitions to Improving Percolation Threshold Bounds","display_name":"The Application of Non-Crossing Partitions to Improving Percolation Threshold Bounds","publication_year":2006,"publication_date":"2006-09-04","ids":{"openalex":"https://openalex.org/W1981225400","doi":"https://doi.org/10.1017/s0963548306007905","mag":"1981225400"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548306007905","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548306007905","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5084779820","display_name":"William D. May","orcid":null},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]},{"id":"https://openalex.org/I2799853436","display_name":"Johns Hopkins Medicine","ror":"https://ror.org/037zgn354","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I2799853436"]},{"id":"https://openalex.org/I6059380","display_name":"University of Baltimore","ror":"https://ror.org/024gw2733","country_code":"US","type":"education","lineage":["https://openalex.org/I6059380"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"WILLIAM D. MAY","raw_affiliation_strings":["Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore MD, USA (e-mail:","Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore MD, USA (e-mail: [email\u00a0protected], [email\u00a0protected])#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore MD, USA (e-mail:","institution_ids":["https://openalex.org/I145311948","https://openalex.org/I2799853436","https://openalex.org/I6059380"]},{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore MD, USA (e-mail: [email\u00a0protected], [email\u00a0protected])#TAB#","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064543263","display_name":"John C. Wierman","orcid":"https://orcid.org/0000-0002-5000-9455"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]},{"id":"https://openalex.org/I2799853436","display_name":"Johns Hopkins Medicine","ror":"https://ror.org/037zgn354","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I2799853436"]},{"id":"https://openalex.org/I6059380","display_name":"University of Baltimore","ror":"https://ror.org/024gw2733","country_code":"US","type":"education","lineage":["https://openalex.org/I6059380"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"JOHN C. WIERMAN","raw_affiliation_strings":["Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore MD, USA (e-mail:","Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore MD, USA (e-mail: [email\u00a0protected], [email\u00a0protected])#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore MD, USA (e-mail:","institution_ids":["https://openalex.org/I145311948","https://openalex.org/I2799853436","https://openalex.org/I6059380"]},{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore MD, USA (e-mail: [email\u00a0protected], [email\u00a0protected])#TAB#","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2832,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.60571698,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"16","issue":"2","first_page":"285","last_page":"307"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12285","display_name":"Surface Chemistry and Catalysis","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12285","display_name":"Surface Chemistry and Catalysis","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9948999881744385,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/percolation","display_name":"Percolation (cognitive psychology)","score":0.7186557054519653},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.6288827657699585},{"id":"https://openalex.org/keywords/percolation-threshold","display_name":"Percolation threshold","score":0.6188467741012573},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49977779388427734},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43921148777008057},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4390026926994324},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3960661292076111},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35867220163345337},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32874301075935364},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.26873353123664856},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.14886590838432312},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07141423225402832},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0646994411945343}],"concepts":[{"id":"https://openalex.org/C2780457167","wikidata":"https://www.wikidata.org/wiki/Q17156484","display_name":"Percolation (cognitive psychology)","level":2,"score":0.7186557054519653},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.6288827657699585},{"id":"https://openalex.org/C2729557","wikidata":"https://www.wikidata.org/wiki/Q7167170","display_name":"Percolation threshold","level":3,"score":0.6188467741012573},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49977779388427734},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43921148777008057},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4390026926994324},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3960661292076111},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35867220163345337},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32874301075935364},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26873353123664856},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.14886590838432312},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07141423225402832},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0646994411945343},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C69990965","wikidata":"https://www.wikidata.org/wiki/Q65402698","display_name":"Electrical resistivity and conductivity","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548306007905","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548306007905","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W172390286","https://openalex.org/W574181710","https://openalex.org/W1602235267","https://openalex.org/W1921768404","https://openalex.org/W1972912363","https://openalex.org/W1977545325","https://openalex.org/W1980918126","https://openalex.org/W1996237450","https://openalex.org/W1999106065","https://openalex.org/W2031535546","https://openalex.org/W2048872268","https://openalex.org/W2066652472","https://openalex.org/W2068593432","https://openalex.org/W2108971721","https://openalex.org/W2115080498","https://openalex.org/W2116824607","https://openalex.org/W2138360701","https://openalex.org/W2146868839","https://openalex.org/W2167266655","https://openalex.org/W4250226066","https://openalex.org/W4256255433","https://openalex.org/W4388296606"],"related_works":["https://openalex.org/W2014145684","https://openalex.org/W1999406914","https://openalex.org/W2060865449","https://openalex.org/W2000145305","https://openalex.org/W2047090164","https://openalex.org/W2077569955","https://openalex.org/W2091600952","https://openalex.org/W1980170026","https://openalex.org/W3103906147","https://openalex.org/W2014221114"],"abstract_inverted_index":{"We":[0,103],"describe":[1],"how":[2],"non-crossing":[3,16],"partitions":[4,17],"arise":[5],"in":[6],"substitution":[7],"method":[8],"calculations.":[9],"By":[10],"using":[11],"efficient":[12],"algorithms":[13],"for":[14,38,109],"computing":[15],"we":[18,47,79],"are":[19],"able":[20],"to":[21,30,57,69,89,101,116],"substantially":[22],"reduce":[23],"the":[24,35,43,65,72,97,106,110],"computational":[25],"effort,":[26],"which":[27],"enables":[28],"us":[29],"compute":[31],"improved":[32],"bounds":[33,49,81],"on":[34],"percolation":[36,40],"thresholds":[37],"three":[39],"models.":[41],"For":[42,71],"Kagom\u00e9":[44],"bond":[45,77],"model":[46,78],"improve":[48,80,105],"from":[50,67,82,99,114],"0.5182":[51],"\u2264":[52,55,59,62,84,87,91,94],"p":[53,60,85,92],"c":[54,61,86,93],"0.5335":[56],"0.522197":[58],"0.526873,":[63],"improving":[64,96],"range":[66,98],"0.0153":[68],"0.004676.":[70],"(3,":[73],"12":[74],"2":[75],")":[76],"0.7393":[83],"0.7418":[88],"0.739773":[90],"0.741125,":[95],"0.0025":[100],"0.001352.":[102],"also":[104],"upper":[107],"bound":[108],"hexagonal":[111],"site":[112],"model,":[113],"0.794717":[115],"0.743359.":[117]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}