{"id":"https://openalex.org/W7220975712","doi":"https://doi.org/10.48550/arxiv.2610.07983","title":"From stylic monoid to Catalan monoid","display_name":"From stylic monoid to Catalan monoid","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220975712","doi":"https://doi.org/10.48550/arxiv.2610.07983"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.07983","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07983","pdf_url":"https://arxiv.org/pdf/2610.07983","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.07983","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087439562","display_name":"Itamar Stein","orcid":"https://orcid.org/0000-0003-3965-0775","observed_orcids":["https://orcid.org/0000-0003-3965-0775"]},"institutions":[{"id":"https://openalex.org/I3129975082","display_name":"Sami Shamoon College of Engineering","ror":"https://ror.org/011aa4g29","country_code":"IL","type":"education","lineage":["https://openalex.org/I3129975082"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Stein, Itamar","raw_affiliation_strings":["Mathematics Unit , Shamoon College of Engineering"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Unit , Shamoon College of Engineering","institution_ids":["https://openalex.org/I3129975082"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5087439562"],"corresponding_institution_ids":["https://openalex.org/I3129975082"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9970999956130981,"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":0.9970999956130981,"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/T11567","display_name":"semigroups and automata theory","score":0.0024999999441206455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/plactic-monoid","display_name":"plactic monoid","score":0.9850000143051147},{"id":"https://openalex.org/keywords/quotient-maps","display_name":"quotient maps","score":0.6430000066757202},{"id":"https://openalex.org/keywords/bijections","display_name":"bijections","score":0.5490000247955322},{"id":"https://openalex.org/keywords/young-tableaux","display_name":"Young tableaux","score":0.593999981880188}],"concepts":[{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.8830000162124634},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.8518000245094299},{"id":"https://openalex.org/C119903167","wikidata":"https://www.wikidata.org/wiki/Q3321297","display_name":"Syntactic monoid","level":4,"score":0.7696999907493591},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.713100016117096},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.644599974155426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5950000286102295},{"id":"https://openalex.org/C149685015","wikidata":"https://www.wikidata.org/wiki/Q5500266","display_name":"Free monoid","level":3,"score":0.5616000294685364},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.5320000052452087},{"id":"https://openalex.org/C43929256","wikidata":"https://www.wikidata.org/wiki/Q270513","display_name":"Catalan number","level":2,"score":0.4968000054359436},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.45750001072883606},{"id":"https://openalex.org/C164105321","wikidata":"https://www.wikidata.org/wiki/Q7026","display_name":"Catalan","level":2,"score":0.42640000581741333},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.42329999804496765},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.3937999904155731},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.37689998745918274},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3756999969482422},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C19787925","wikidata":"https://www.wikidata.org/wiki/Q619436","display_name":"Quotient ring","level":4,"score":0.2759999930858612},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27219998836517334}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.07983","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07983","pdf_url":"https://arxiv.org/pdf/2610.07983","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.07983","doi":"https://doi.org/10.48550/arxiv.2610.07983","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.07983","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.07983","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07983","pdf_url":"https://arxiv.org/pdf/2610.07983","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220975712.pdf","grobid_xml":"https://content.openalex.org/works/W7220975712.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2808679602","https://openalex.org/W7213372456"],"related_works":["https://openalex.org/W4281846588","https://openalex.org/W7111636084","https://openalex.org/W4289262009","https://openalex.org/W4311658443","https://openalex.org/W7213372456","https://openalex.org/W2808679602","https://openalex.org/W4390659701","https://openalex.org/W4399803900","https://openalex.org/W2582724091","https://openalex.org/W7099492967"],"abstract_inverted_index":{"The":[0,94],"stylic":[1],"monoid":[2,15,32],"$\\mathrm{Styl}_n$,":[3],"introduced":[4],"by":[5,16,25,203],"Abram":[6],"and":[7,20,53,85,142,188,244],"Reutenauer,":[8],"is":[9,40,49,55,97,152,181],"the":[10,13,17,30,46,64,92,114,124,145,156,168,174,190,196,207,226,232,250],"quotient":[11,42,47,169],"of":[12,34,38,43,87,116,193,198],"plactic":[14],"relations":[18],"$x^2=x$,":[19],"its":[21,88,218],"elements":[22],"are":[23,239],"represented":[24],"$N$-tableaux.":[26],"Volkov":[27],"showed":[28],"that":[29,98,144,201,223,236],"Catalan":[31],"$\\mathrm{Cat}_n$":[33,67],"order-preserving,":[35],"order-decreasing":[36],"self-maps":[37],"$\\{0,1,\\ldots,n\\}$":[39],"a":[41,76,108,134,140,255],"$\\mathrm{Styl}_n$.":[44],"However,":[45],"map":[48,65,252],"defined":[50],"on":[51,103],"generators,":[52],"it":[54,68,216],"not":[56,101,230],"apparent":[57],"how":[58,247],"to":[59,80,119,123,155,166,225,248],"see,":[60],"from":[61,91,149,206],"an":[62,105,194,212],"$N$-tableau,":[63],"in":[66,177,234,240],"corresponds":[69],"to.":[70],"In":[71],"this":[72,83,139],"paper":[73],"we":[74,99,112,245],"give":[75],"simple":[77],"visual":[78],"way":[79],"read":[81,148,249],"off":[82,254],"map,":[84],"some":[86],"main":[89],"properties,":[90],"$N$-tableau.":[93,257],"new":[95],"ingredient":[96],"do":[100],"insist":[102],"drawing":[104],"$N$-tableau":[106,213],"as":[107,127,129,183,186],"classical":[109],"Young":[110],"tableau:":[111],"allow":[113],"entries":[115],"each":[117,130,179,199],"row":[118,125],"be":[120,164],"shifted":[121],"relative":[122],"below,":[126],"long":[128],"entry":[131,180],"stays":[132],"above":[133],"smaller":[135],"one.":[136],"We":[137,171,210,221],"call":[138,211],"positioning,":[141,176],"prove":[143,222],"column":[146,158,200],"word":[147],"any":[150],"positioning":[151,162],"plactically":[153],"equivalent":[154],"usual":[157],"word;":[159],"so":[160],"every":[161],"can":[163],"used":[165],"compute":[167],"map.":[170],"work":[172],"with":[173,242],"tight":[175],"which":[178],"pushed":[182],"far":[184],"right":[185],"possible,":[187],"define":[189],"full":[191,214,219,227,237,256],"core":[192,228],"$N$-tableau:":[195],"part":[197],"climbs":[202],"consecutive":[204],"values":[205],"bottom":[208],"row.":[209],"if":[215],"equals":[217],"core.":[220],"passing":[224],"does":[229],"change":[231],"image":[233],"$\\mathrm{Cat}_n$,":[235,243],"$N$-tableaux":[238],"bijection":[241],"show":[246],"corresponding":[251],"directly":[253]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}
