{"id":"https://openalex.org/W7214725787","doi":"https://doi.org/10.48550/arxiv.2609.33732","title":"Strong $q$-log-convexity of the $d$-Hoggatt polynomials","display_name":"Strong $q$-log-convexity of the $d$-Hoggatt polynomials","publication_year":2026,"publication_date":"2026-09-27","ids":{"openalex":"https://openalex.org/W7214725787","doi":"https://doi.org/10.48550/arxiv.2609.33732"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.33732","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33732","pdf_url":"https://arxiv.org/pdf/2609.33732","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/2609.33732","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057947204","display_name":"Shane Chern","orcid":"https://orcid.org/0000-0002-8321-1895","observed_orcids":["https://orcid.org/0000-0002-8321-1895"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chern, Shane","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102438012","display_name":"Wenle Shi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi, Wenle","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":2,"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":0.9711999893188477,"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":0.9711999893188477,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.020999999716877937,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.006599999964237213,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/q-analogues","display_name":"q-analogues","score":0.7870000004768372},{"id":"https://openalex.org/keywords/schur-polynomials","display_name":"Schur functions","score":0.8500000238418579}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6992999911308289},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5990999937057495},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46810001134872437},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42899999022483826},{"id":"https://openalex.org/C146922319","wikidata":"https://www.wikidata.org/wiki/Q4298935","display_name":"Schur polynomial","level":5,"score":0.4207000136375427},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.4156000018119812},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.41519999504089355},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.3774999976158142},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.375900000333786},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.3643999993801117},{"id":"https://openalex.org/C171686973","wikidata":"https://www.wikidata.org/wiki/Q17098676","display_name":"Macdonald polynomials","level":4,"score":0.3303000032901764},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32519999146461487},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.32199999690055847},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.26499998569488525},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.26019999384880066},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.33732","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33732","pdf_url":"https://arxiv.org/pdf/2609.33732","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.2609.33732","doi":"https://doi.org/10.48550/arxiv.2609.33732","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.33732","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:2609.33732","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33732","pdf_url":"https://arxiv.org/pdf/2609.33732","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":[{"id":"https://openalex.org/G2367598221","display_name":"Discrete random structures: enumeration and scaling limits","funder_award_id":"F 1002","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G9000308504","display_name":null,"funder_award_id":"10.55776/F1002","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214725787.pdf","grobid_xml":"https://content.openalex.org/works/W7214725787.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1275244816","https://openalex.org/W3134498533","https://openalex.org/W7167227897","https://openalex.org/W7204165078"],"related_works":["https://openalex.org/W2971974020","https://openalex.org/W1548205923","https://openalex.org/W2953301595","https://openalex.org/W1894738992","https://openalex.org/W7098443325","https://openalex.org/W2151257138","https://openalex.org/W2071670791","https://openalex.org/W2564105279","https://openalex.org/W1541557855","https://openalex.org/W7096538479"],"abstract_inverted_index":{"In":[0],"this":[1,47],"paper,":[2],"three":[3],"($q$-)log-convexity":[4],"or":[5],"concavity":[6],"properties":[7],"related":[8],"to":[9],"the":[10,19,23,31,43,50,60],"$d$-Hoggatt":[11,20,38,53],"numbers":[12],"are":[13],"investigated.":[14],"First,":[15],"we":[16,41],"show":[17],"that":[18],"transformation":[21],"preserves":[22],"log-convexity":[24],"of":[25,34,37,46,52,62],"a":[26,35],"sequence.":[27],"We":[28],"then":[29],"establish":[30],"strong":[32],"$q$-log-concavity":[33],"$q$-analog":[36],"numbers.":[39],"Finally,":[40],"prove":[42],"core":[44],"result":[45],"work,":[48],"namely,":[49],"sequence":[51],"polynomials":[54],"is":[55],"strongly":[56],"$q$-log-convex,":[57],"based":[58],"on":[59],"theory":[61],"Schur":[63],"functions.":[64]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}