{"id":"https://openalex.org/W4414929342","doi":"https://doi.org/10.1016/j.aam.2025.102979","title":"Hybrid pipe dreams for key polynomials","display_name":"Hybrid pipe dreams for key polynomials","publication_year":2025,"publication_date":"2025-10-08","ids":{"openalex":"https://openalex.org/W4414929342","doi":"https://doi.org/10.1016/j.aam.2025.102979"},"language":"en","primary_location":{"id":"doi:10.1016/j.aam.2025.102979","doi":"https://doi.org/10.1016/j.aam.2025.102979","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.aam.2025.102979","pdf_url":null,"source":{"id":"https://openalex.org/S164906323","display_name":"Advances in Applied Mathematics","issn_l":"0196-8858","issn":["0196-8858","1090-2074"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Applied Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.aam.2025.102979","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Yihan Xiao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yihan Xiao","raw_affiliation_strings":["Department of Mathematics, College of Sciences, Shanghai University, 99 Shangda Road, Baoshan District, Shanghai, 200444, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Sciences, Shanghai University, 99 Shangda Road, Baoshan District, Shanghai, 200444, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035055273","display_name":"Rui Xiong","orcid":"https://orcid.org/0000-0001-8025-0795","observed_orcids":["https://orcid.org/0000-0001-8025-0795"]},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Rui Xiong","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Ottawa, 150 Louis-Pasteur, Ottawa, ON K1N 6N5, Canada"],"raw_orcid":"https://orcid.org/0000-0001-8025-0795","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, 150 Louis-Pasteur, Ottawa, ON K1N 6N5, Canada","institution_ids":["https://openalex.org/I153718931"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064008061","display_name":"Haofeng Zhang","orcid":"https://orcid.org/0000-0002-4039-7618","observed_orcids":["https://orcid.org/0000-0002-4039-7618"]},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haofeng Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Peking University, 5 Yiheyuan Road, Haidian District, Beijing, 100871, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Peking University, 5 Yiheyuan Road, Haidian District, Beijing, 100871, China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035055273"],"corresponding_institution_ids":["https://openalex.org/I153718931"],"apc_list":{"value":3380,"currency":"USD","value_usd":3380},"apc_paid":{"value":3380,"currency":"USD","value_usd":3380},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"173","issue":null,"first_page":"102979","last_page":"102979"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":1.0,"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":1.0,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.0,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/key-polynomials","display_name":"key polynomials","score":1.0},{"id":"https://openalex.org/keywords/pipe-dreams","display_name":"pipe dreams","score":0.6930000185966492},{"id":"https://openalex.org/keywords/schubert-polynomials","display_name":"Schubert polynomials","score":0.9710000157356262},{"id":"https://openalex.org/keywords/combinatorial-models","display_name":"combinatorial models","score":0.8849999904632568},{"id":"https://openalex.org/keywords/young-tableaux","display_name":"Young tableaux","score":0.7369999885559082},{"id":"https://openalex.org/keywords/littlewood-richardson-rule","display_name":"Littlewood-Richardson rule","score":0.7879999876022339}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7907999753952026},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.635699987411499},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5135999917984009},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4438000023365021},{"id":"https://openalex.org/C2781095916","wikidata":"https://www.wikidata.org/wiki/Q36348","display_name":"Dream","level":2,"score":0.39730000495910645},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32989999651908875},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3239000141620636},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3172999918460846},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.2879999876022339},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2644999921321869}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/j.aam.2025.102979","doi":"https://doi.org/10.1016/j.aam.2025.102979","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.aam.2025.102979","pdf_url":null,"source":{"id":"https://openalex.org/S164906323","display_name":"Advances in Applied Mathematics","issn_l":"0196-8858","issn":["0196-8858","1090-2074"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2411.01637","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2411.01637","pdf_url":"https://arxiv.org/pdf/2411.01637","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2411.01637","doi":"https://doi.org/10.48550/arxiv.2411.01637","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2411.01637","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1016/j.aam.2025.102979","doi":"https://doi.org/10.1016/j.aam.2025.102979","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.aam.2025.102979","pdf_url":null,"source":{"id":"https://openalex.org/S164906323","display_name":"Advances in Applied Mathematics","issn_l":"0196-8858","issn":["0196-8858","1090-2074"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414929342.pdf","grobid_xml":"https://content.openalex.org/works/W4414929342.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W33780762","https://openalex.org/W178893740","https://openalex.org/W1502291261","https://openalex.org/W1511084141","https://openalex.org/W1657002161","https://openalex.org/W1963575111","https://openalex.org/W1964281812","https://openalex.org/W1990770892","https://openalex.org/W1995152055","https://openalex.org/W2000642568","https://openalex.org/W2010704230","https://openalex.org/W2013404833","https://openalex.org/W2024473946","https://openalex.org/W2064031190","https://openalex.org/W2064558129","https://openalex.org/W2080720229","https://openalex.org/W2094594266","https://openalex.org/W2117804714","https://openalex.org/W2127707637","https://openalex.org/W2134984950","https://openalex.org/W2276720166","https://openalex.org/W2294841707","https://openalex.org/W2417980922","https://openalex.org/W2520741081","https://openalex.org/W2559215801","https://openalex.org/W2573960099","https://openalex.org/W2594342427","https://openalex.org/W2618078593","https://openalex.org/W2731933298","https://openalex.org/W2753855571","https://openalex.org/W2806526379","https://openalex.org/W2810109868","https://openalex.org/W2939922548","https://openalex.org/W2969507140","https://openalex.org/W2969989209","https://openalex.org/W2977437121","https://openalex.org/W2981125629","https://openalex.org/W2983189712","https://openalex.org/W3098374937","https://openalex.org/W3119544636","https://openalex.org/W4287020903","https://openalex.org/W4321492388","https://openalex.org/W4381251264","https://openalex.org/W4387394542","https://openalex.org/W4416301832"],"related_works":["https://openalex.org/W4416697921","https://openalex.org/W3115109098","https://openalex.org/W6960054789","https://openalex.org/W3090609520","https://openalex.org/W1995152055","https://openalex.org/W7097813105","https://openalex.org/W4404407592","https://openalex.org/W7063842582","https://openalex.org/W4408356921","https://openalex.org/W1659324170"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2],"family":[3],"of":[4],"new":[5],"combinatorial":[6],"models":[7],"for":[8,20],"key":[9],"polynomials.":[10],"It":[11],"is":[12],"similar":[13],"to":[14],"the":[15],"hybrid":[16],"pipe":[17],"dream":[18],"model":[19],"Schubert":[21],"polynomials":[22],"defined":[23],"recently":[24],"by":[25],"Knutson":[26],"and":[27],"Udell.":[28]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2025-10-10T00:00:00"}
