{"id":"https://openalex.org/W2106381322","doi":"https://doi.org/10.37236/125","title":"Optimal Betti Numbers of Forest Ideals","display_name":"Optimal Betti Numbers of Forest Ideals","publication_year":2009,"publication_date":"2009-03-13","ids":{"openalex":"https://openalex.org/W2106381322","doi":"https://doi.org/10.37236/125","mag":"2106381322"},"language":"en","primary_location":{"id":"doi:10.37236/125","is_oa":true,"landing_page_url":"https://doi.org/10.37236/125","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r36/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r36/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043122287","display_name":"Michael Goff","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael Goff","raw_affiliation_strings":["Department of Mathematics University of Washington, Seattle, WA 98195-4350, USA","University of Washington"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Washington, Seattle, WA 98195-4350, USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043122287"],"corresponding_institution_ids":["https://openalex.org/I201448701"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19048863,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":1.0,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.989300012588501,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9646000266075134,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/betti-number","display_name":"Betti number","score":0.9664903879165649},{"id":"https://openalex.org/keywords/square-free-integer","display_name":"Square-free integer","score":0.9475499987602234},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9172441959381104},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.7836338877677917},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.671022891998291},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5796606540679932},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4847578704357147},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4687160551548004},{"id":"https://openalex.org/keywords/monomial-ideal","display_name":"Monomial ideal","score":0.42109981179237366},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38594135642051697},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.0832814872264862},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06537991762161255}],"concepts":[{"id":"https://openalex.org/C129621563","wikidata":"https://www.wikidata.org/wiki/Q429593","display_name":"Betti number","level":2,"score":0.9664903879165649},{"id":"https://openalex.org/C188139237","wikidata":"https://www.wikidata.org/wiki/Q50706","display_name":"Square-free integer","level":2,"score":0.9475499987602234},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9172441959381104},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.7836338877677917},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.671022891998291},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5796606540679932},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4847578704357147},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4687160551548004},{"id":"https://openalex.org/C2777789435","wikidata":"https://www.wikidata.org/wiki/Q19369206","display_name":"Monomial ideal","level":4,"score":0.42109981179237366},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38594135642051697},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.0832814872264862},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06537991762161255},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/125","is_oa":true,"landing_page_url":"https://doi.org/10.37236/125","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r36/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.214.4560","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.4560","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_16/PDF/v16i1r36.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.311.6821","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.311.6821","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0809.0156v1.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/125","is_oa":true,"landing_page_url":"https://doi.org/10.37236/125","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r36/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.5799999833106995}],"awards":[{"id":"https://openalex.org/G1861464123","display_name":"Around the theory of f-vectors","funder_award_id":"0801152","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5234711165","display_name":"EMSW21-VIGRE: Vertical and Horizontal Integration of the Mathematical Sciences at the University of Washington","funder_award_id":"0354131","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2106381322.pdf","grobid_xml":"https://content.openalex.org/works/W2106381322.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1495486040","https://openalex.org/W1509308325","https://openalex.org/W1515761639","https://openalex.org/W1537258143","https://openalex.org/W1573607435","https://openalex.org/W1977775383","https://openalex.org/W1981399571","https://openalex.org/W1992807466","https://openalex.org/W1993748105","https://openalex.org/W2004751842","https://openalex.org/W2027883704","https://openalex.org/W2052514409","https://openalex.org/W2069797376","https://openalex.org/W2079836066","https://openalex.org/W2089328508","https://openalex.org/W2092971872","https://openalex.org/W2104532376","https://openalex.org/W2111230986","https://openalex.org/W2134506831","https://openalex.org/W2952991990","https://openalex.org/W2964032069","https://openalex.org/W3107709063","https://openalex.org/W4285719527","https://openalex.org/W6611252610","https://openalex.org/W6819858357"],"related_works":["https://openalex.org/W1588275287","https://openalex.org/W4300710561","https://openalex.org/W2952279733","https://openalex.org/W2175341027","https://openalex.org/W2069932879","https://openalex.org/W1875848822","https://openalex.org/W4293584813","https://openalex.org/W4214563470","https://openalex.org/W2946572018","https://openalex.org/W4288359629"],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2],"tight":[3],"lower":[4],"bound":[5,19],"on":[6,20],"the":[7],"algebraic":[8],"Betti":[9,23],"numbers":[10,24],"of":[11,25],"tree":[12],"and":[13,16],"forest":[14],"ideals":[15],"an":[17],"upper":[18],"certain":[21],"graded":[22],"squarefree":[26],"monomial":[27],"ideals.":[28]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
