{"id":"https://openalex.org/W2092855545","doi":"https://doi.org/10.1016/s0012-365x(01)00251-5","title":"Shifted quasi-symmetric functions and the Hopf algebra of peak functions","display_name":"Shifted quasi-symmetric functions and the Hopf algebra of peak functions","publication_year":2002,"publication_date":"2002-03-01","ids":{"openalex":"https://openalex.org/W2092855545","doi":"https://doi.org/10.1016/s0012-365x(01)00251-5","mag":"2092855545"},"language":"en","primary_location":{"id":"doi:10.1016/s0012-365x(01)00251-5","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(01)00251-5","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/9904105","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037352600","display_name":"Nantel Bergeron","orcid":"https://orcid.org/0000-0002-4482-7427"},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Nantel Bergeron","raw_affiliation_strings":["Department of Mathematics and Statistics, York University, Toronto, Ont. Canada, M3J 1P3","Department of Mathematics and Statistics, York University, Toronto, Ont. Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, Ont. Canada, M3J 1P3","institution_ids":["https://openalex.org/I192455969"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, Ont. Canada#TAB#","institution_ids":["https://openalex.org/I192455969"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078006471","display_name":"Stefan Mykytiuk","orcid":null},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Stefan Mykytiuk","raw_affiliation_strings":["Department of Mathematics and Statistics, York University, Toronto, Ont. Canada, M3J 1P3","Department of Mathematics and Statistics, York University, Toronto, Ont. Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, Ont. Canada, M3J 1P3","institution_ids":["https://openalex.org/I192455969"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, Ont. Canada#TAB#","institution_ids":["https://openalex.org/I192455969"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078229263","display_name":"Frank Sottile","orcid":"https://orcid.org/0000-0003-0087-7120"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Frank Sottile","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison, WI. 53706-1388, USA","Department of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison, WI#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison, WI. 53706-1388, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison, WI#TAB#","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056815498","display_name":"Stephanie van Willigenburg","orcid":"https://orcid.org/0000-0002-5340-5568"},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Stephanie van Willigenburg","raw_affiliation_strings":["Department of Mathematics and Statistics, York University, Toronto, Ont. Canada, M3J 1P3","Department of Mathematics and Statistics, York University, Toronto, Ont. Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, Ont. Canada, M3J 1P3","institution_ids":["https://openalex.org/I192455969"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, Ont. Canada#TAB#","institution_ids":["https://openalex.org/I192455969"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5037352600"],"corresponding_institution_ids":["https://openalex.org/I192455969"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":3.5032,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.92487752,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"246","issue":"1-3","first_page":"57","last_page":"66"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998999834060669,"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":0.9998999834060669,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.791827917098999},{"id":"https://openalex.org/keywords/hopf-algebra","display_name":"Hopf algebra","score":0.6403391361236572},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.6054261326789856},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.5781792998313904},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5301643013954163},{"id":"https://openalex.org/keywords/subalgebra","display_name":"Subalgebra","score":0.4658884108066559},{"id":"https://openalex.org/keywords/schubert-polynomial","display_name":"Schubert polynomial","score":0.4359566271305084},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3862406611442566},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37917813658714294}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.791827917098999},{"id":"https://openalex.org/C29712632","wikidata":"https://www.wikidata.org/wiki/Q1627597","display_name":"Hopf algebra","level":3,"score":0.6403391361236572},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.6054261326789856},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.5781792998313904},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5301643013954163},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.4658884108066559},{"id":"https://openalex.org/C97912942","wikidata":"https://www.wikidata.org/wiki/Q7432937","display_name":"Schubert polynomial","level":2,"score":0.4359566271305084},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3862406611442566},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37917813658714294}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/s0012-365x(01)00251-5","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(01)00251-5","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/9904105","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/9904105","pdf_url":"https://arxiv.org/pdf/math/9904105","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:CiteSeerX.psu:10.1.1.11.7145","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.7145","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathe2.uni-bayreuth.de/axel/papers/./sottile:shifted_quasi_symmetric_functions_and_the_hopf_algebra_of_peak_functions.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.9.3237","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.9.3237","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.umass.edu/~sottile/ps/shifted.ps.gz","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/9904105","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/9904105","pdf_url":"https://arxiv.org/pdf/math/9904105","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1524155628","https://openalex.org/W2010073471","https://openalex.org/W2024806284","https://openalex.org/W2128924961","https://openalex.org/W2133946641","https://openalex.org/W2156535181","https://openalex.org/W2499069110","https://openalex.org/W4241107612"],"related_works":["https://openalex.org/W2062169824","https://openalex.org/W58946223","https://openalex.org/W2392481465","https://openalex.org/W4299351395","https://openalex.org/W2276776477","https://openalex.org/W2133945002","https://openalex.org/W3175259534","https://openalex.org/W3103934915","https://openalex.org/W3136872684","https://openalex.org/W2089856470"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
