{"id":"https://openalex.org/W627005472","doi":null,"title":"Graphical representations of the $q$-creation and the $q$-annihilation operators and set partition statistics (Infinite Dimensional Analysis and Quantum Probability Theory)","display_name":"Graphical representations of the $q$-creation and the $q$-annihilation operators and set partition statistics (Infinite Dimensional Analysis and Quantum Probability Theory)","publication_year":2001,"publication_date":"2001-08-01","ids":{"openalex":"https://openalex.org/W627005472","mag":"627005472"},"language":"en","primary_location":{"id":"pmh:oai:irdb.nii.ac.jp:01221:0000011737","doi":null,"is_oa":true,"landing_page_url":"https://repository.kulib.kyoto-u.ac.jp/bitstreams/1f073685-6846-45f7-8b4f-ca9a999499b0/download","pdf_url":"https://repository.kulib.kyoto-u.ac.jp/bitstreams/1f073685-6846-45f7-8b4f-ca9a999499b0/download","source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"\u6570\u7406\u89e3\u6790\u7814\u7a76\u6240\u8b1b\u7a76\u9332","raw_type":"departmental bulletin paper"},"volume":null,"type":"article","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://repository.kulib.kyoto-u.ac.jp/bitstreams/1f073685-6846-45f7-8b4f-ca9a999499b0/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073098982","display_name":"Hiroaki Yoshida","orcid":"https://orcid.org/0000-0002-5370-7451","observed_orcids":["https://orcid.org/0000-0002-5370-7451"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hiroaki Yoshida","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5370-7451","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5073098982"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06141367,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"1227","issue":null,"first_page":"218","last_page":"229"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.7153000235557556,"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":0.7153000235557556,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.11959999799728394,"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"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.02329999953508377,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/graphical-representation","display_name":"graphical representation","score":0.7590000033378601},{"id":"https://openalex.org/keywords/q-deformation","display_name":"q-deformation","score":0.6899999976158142},{"id":"https://openalex.org/keywords/free-probability","display_name":"free probability","score":0.7630000114440918},{"id":"https://openalex.org/keywords/non-crossing-partitions","display_name":"noncrossing partitions","score":0.5230000019073486}],"concepts":[{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6186665892601013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5088077187538147},{"id":"https://openalex.org/C201941533","wikidata":"https://www.wikidata.org/wiki/Q188721","display_name":"Annihilation","level":2,"score":0.49901676177978516},{"id":"https://openalex.org/C63630878","wikidata":"https://www.wikidata.org/wiki/Q902336","display_name":"Creation and annihilation operators","level":3,"score":0.4800530672073364},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45953062176704407},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.41725850105285645},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3829192817211151},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.34591788053512573},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3301572799682617},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.27296513319015503},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2720358967781067},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26447203755378723},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:irdb.nii.ac.jp:01221:0000011737","doi":null,"is_oa":true,"landing_page_url":"https://repository.kulib.kyoto-u.ac.jp/bitstreams/1f073685-6846-45f7-8b4f-ca9a999499b0/download","pdf_url":"https://repository.kulib.kyoto-u.ac.jp/bitstreams/1f073685-6846-45f7-8b4f-ca9a999499b0/download","source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"\u6570\u7406\u89e3\u6790\u7814\u7a76\u6240\u8b1b\u7a76\u9332","raw_type":"departmental bulletin paper"},{"id":"pmh:oai:repository.kulib.kyoto-u.ac.jp:2433/41416","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/2433/41416","pdf_url":"http://hdl.handle.net/2433/41416","source":{"id":"https://openalex.org/S4306401454","display_name":"Kyoto University Research Information Repository (Kyoto University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I22299242","host_organization_name":"Kyoto University","host_organization_lineage":["https://openalex.org/I22299242"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Departmental Bulletin Paper"},{"id":"mag:627005472","doi":null,"is_oa":false,"landing_page_url":"https://repository.kulib.kyoto-u.ac.jp/dspace/handle/2433/41416","pdf_url":null,"source":{"id":"https://openalex.org/S4306549803","display_name":"\u6570\u7406\u89e3\u6790\u7814\u7a76\u6240\u8b1b\u7a76\u9332","issn_l":"1880-2818","issn":["1880-2818","2760-7046"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"\u6570\u7406\u89e3\u6790\u7814\u7a76\u6240\u8b1b\u7a76\u9332","raw_type":null}],"best_oa_location":{"id":"pmh:oai:irdb.nii.ac.jp:01221:0000011737","doi":null,"is_oa":true,"landing_page_url":"https://repository.kulib.kyoto-u.ac.jp/bitstreams/1f073685-6846-45f7-8b4f-ca9a999499b0/download","pdf_url":"https://repository.kulib.kyoto-u.ac.jp/bitstreams/1f073685-6846-45f7-8b4f-ca9a999499b0/download","source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"\u6570\u7406\u89e3\u6790\u7814\u7a76\u6240\u8b1b\u7a76\u9332","raw_type":"departmental bulletin paper"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4392737251","https://openalex.org/W1987937869","https://openalex.org/W2514536269","https://openalex.org/W4293816529","https://openalex.org/W2981167813","https://openalex.org/W2139218683","https://openalex.org/W7099530649","https://openalex.org/W7145799090","https://openalex.org/W6891972901","https://openalex.org/W2951743819"],"abstract_inverted_index":{"In":[0],"this":[1],"note,":[2],"we":[3,78,179],"introduce":[4],"acertain":[5],"graphical":[6],"representations":[7],"of":[8,40,43,58,65,82,90,163,165,203],"the":[9,11,13,17,21,27,41,51,62,66,70,80,83,88,95,116,119,124,143,160,166,192,200],"$q$-creation":[10],"$q$-annihilation,":[12],"$q$-numb":[14],"er,":[15],"and":[16,36,38,48,118,140,178],"scalar":[18],"operators":[19],"on":[20,29,196],"$q$-Fock":[22,144],"space.These":[23],"are":[24,34],"given":[25,198],"as":[26,64,100,150],"cards":[28,52],"which":[30,59,93,113],"some":[31,185],"flow":[32],"lines":[33,44],"drawn":[35],"increasing":[37],"decreasing":[39],"number":[42,89],"correspond":[45],"to":[46],"creation":[47],"annihilation,":[49],"respectively.By":[50],"arrangement":[53],"technique":[54],"with":[55,127],"these":[56],"cards,":[57],"machinery":[60],"is":[61,94,123],"same":[63,96],"partition":[67,98],"function":[68],"for":[69,153,184],"lattice":[71],"spins":[72],"model":[73],"in":[74,175],"statistical":[75],"me-":[76],"chanics,":[77],"write":[79],"moments":[81],"$q$-Poisson":[84],"random":[85],"variable":[86],"using":[87],"arc":[91],"crossings,":[92],"set":[97],"statistic":[99],"restricted":[101],"crossings":[102],"investigated":[103],"by":[104,199],"P.":[105],"Biane.This":[106],"result":[107],"suggests":[108],"another":[109],"$q$-deformed":[110],"moments-cumulants":[111],"relations,":[112],"interpolates":[114],"between":[115],"usual":[117],"free":[120],"cases":[121],"exactly.This":[122],"joint":[125],"work":[126],"Naoko":[128],"Saitoh":[129],"at":[130],"Ochanomizu":[131],"University.1The":[132],"$q$":[133],"-Fock":[134],"space":[135,138,145],"For":[136],"aHibert":[137],"7{":[139],"$q\\in(-1,1)$":[141],",":[142,171,206],"$\\mathcal{F}_{q}(\\mathcal{H})$":[146],"can":[147],"be":[148,159],"defined":[149],"follows:":[151],"(see,":[152],"instance,":[154],"[BS1],":[155],"[BKS])":[156],"Let":[157],"$\\mathcal{F}^{fin}(\\mathcal{H})$":[158],"linear":[161],"span":[162],"vectors":[164],"form":[167,194],"$\\xi_{1}\\otimes\\cdots\\otimes\\xi_{n}\\in":[168],"\\mathcal{H}^{\\otimes":[169],"n}$":[170],"where":[172],"$n$":[173],"varies":[174],"$\\mathrm{z}_{\\geq":[176],"0}$":[177],"put":[180],"$\\mathcal{H}^{\\otimes":[181],"0}\\cong":[182],"\\mathrm{C}\\Omega$":[183],"distinguished":[186],"vector":[187],"$\\Omega$":[188],"called":[189],"vacuum.We":[190],"consider":[191],"sesquilinear":[193,201],"$\\langle\\cdot|\\cdot\\rangle_{q}$":[195],"$\\mathcal{F}^{J^{jn}}(\\mathcal{H})$":[197],"extension":[202],"$\\langle\\xi_{1}\\otimes\\cdots\\otimes\\xi_{n}|\\eta_{1}\\otimes\\cdots\\otimes\\eta_{m}\\rangle_{q}=\\delta_{n,m}\\sum_{\\pi\\in":[204],"S_{n}}q^{i(\\pi)}\\langle\\xi_{1}|\\eta_{\\pi(1)}\\rangle\\cdots\\langle\\xi_{n}|\\eta_{\\pi(n)}\\rangle$":[205]},"counts_by_year":[],"updated_date":"2026-09-11T09:22:31.653822","created_date":"2016-06-24T00:00:00"}