{"id":"https://openalex.org/W7224002196","doi":"https://doi.org/10.48550/arxiv.2610.34982","title":"Exponentially large mu-coefficients","display_name":"Exponentially large mu-coefficients","publication_year":2026,"publication_date":"2026-10-26","ids":{"openalex":"https://openalex.org/W7224002196","doi":"https://doi.org/10.48550/arxiv.2610.34982"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.34982","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34982","pdf_url":"https://arxiv.org/pdf/2610.34982","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.34982","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092071942","display_name":"Tom Goertzen","orcid":"https://orcid.org/0009-0003-3399-3416","observed_orcids":["https://orcid.org/0009-0003-3399-3416"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Goertzen, Tom","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075961654","display_name":"Abel Lacabanne","orcid":"https://orcid.org/0000-0001-8691-3270","observed_orcids":["https://orcid.org/0000-0001-8691-3270"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lacabanne, Abel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016692246","display_name":"Daniel Tubbenhauer","orcid":"https://orcid.org/0000-0001-7265-5047","observed_orcids":["https://orcid.org/0000-0001-7265-5047"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tubbenhauer, Daniel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5032275084","display_name":"Pedro Vaz","orcid":"https://orcid.org/0000-0001-9422-4707","observed_orcids":["https://orcid.org/0000-0001-9422-4707"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vaz, Pedro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":0.9990000128746033,"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":0.9990000128746033,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0003000000142492354,"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/T10849","display_name":"Finite Group Theory Research","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/kazhdan-lusztig-polynomials","display_name":"Kazhdan-Lusztig polynomials","score":0.9589999914169312},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"symmetric group","score":0.9430000185966492},{"id":"https://openalex.org/keywords/world-wide-web","display_name":"World Wide Web","score":0.8320000171661377},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"exponential growth","score":0.8610000014305115},{"id":"https://openalex.org/keywords/rank","display_name":"RANK","score":0.4259999990463257},{"id":"https://openalex.org/keywords/young-tableaux","display_name":"Young tableaux","score":0.5820000171661377}],"concepts":[{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.6801000237464905},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5544000267982483},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35659998655319214},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.33799999952316284},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3154999911785126},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30570000410079956},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2939999997615814},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2578999996185303}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.34982","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34982","pdf_url":"https://arxiv.org/pdf/2610.34982","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.2610.34982","doi":"https://doi.org/10.48550/arxiv.2610.34982","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.34982","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:2610.34982","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34982","pdf_url":"https://arxiv.org/pdf/2610.34982","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/W7224002196.pdf","grobid_xml":"https://content.openalex.org/works/W7224002196.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2949912684","https://openalex.org/W7100542405","https://openalex.org/W7096214652","https://openalex.org/W7098974965","https://openalex.org/W6990886736","https://openalex.org/W2146140985","https://openalex.org/W7097999416","https://openalex.org/W2083216994","https://openalex.org/W2795645228","https://openalex.org/W4317380817"],"abstract_inverted_index":{"Using":[0],"webs,":[1],"we":[2],"prove":[3],"that":[4],"Kazhdan-Lusztig":[5],"mu-coefficients":[6],"for":[7,18],"symmetric":[8],"groups":[9],"grow":[10],"at":[11],"least":[12],"exponentially":[13],"with":[14],"the":[15],"rank,":[16],"already":[17],"pairs":[19],"labeled":[20],"by":[21],"a":[22],"three-row":[23],"rectangle.":[24]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2026-10-28T00:00:00"}