{"id":"https://openalex.org/W2157555182","doi":"https://doi.org/10.37236/171","title":"Updown Numbers and the Initial Monomials of the Slope Variety","display_name":"Updown Numbers and the Initial Monomials of the Slope Variety","publication_year":2009,"publication_date":"2009-07-09","ids":{"openalex":"https://openalex.org/W2157555182","doi":"https://doi.org/10.37236/171","mag":"2157555182"},"language":"en","primary_location":{"id":"doi:10.37236/171","is_oa":true,"landing_page_url":"https://doi.org/10.37236/171","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r82/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/v16i1r82/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057471662","display_name":"Jeremy L. Martin","orcid":"https://orcid.org/0000-0002-3034-5486"},"institutions":[{"id":"https://openalex.org/I146416000","display_name":"University of Kansas","ror":"https://ror.org/001tmjg57","country_code":"US","type":"education","lineage":["https://openalex.org/I146416000"]},{"id":"https://openalex.org/I127339705","display_name":"Washburn University","ror":"https://ror.org/04sk2ar21","country_code":"US","type":"education","lineage":["https://openalex.org/I127339705"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jeremy L. Martin","raw_affiliation_strings":["Department of Mathematics University of Kansas Lawrence, KS 66047 USA","Department of Mathematics and Statistics Washburn University Topeka, KS 66621, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Kansas Lawrence, KS 66047 USA","institution_ids":["https://openalex.org/I146416000"]},{"raw_affiliation_string":"Department of Mathematics and Statistics Washburn University Topeka, KS 66621, USA","institution_ids":["https://openalex.org/I127339705"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018021243","display_name":"Jennifer D. Wagner","orcid":null},"institutions":[{"id":"https://openalex.org/I146416000","display_name":"University of Kansas","ror":"https://ror.org/001tmjg57","country_code":"US","type":"education","lineage":["https://openalex.org/I146416000"]},{"id":"https://openalex.org/I127339705","display_name":"Washburn University","ror":"https://ror.org/04sk2ar21","country_code":"US","type":"education","lineage":["https://openalex.org/I127339705"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jennifer D. Wagner","raw_affiliation_strings":["Department of Mathematics and Statistics Washburn University Topeka, KS 66621, USA","Department of Mathematics University of Kansas Lawrence, KS 66047 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics Washburn University Topeka, KS 66621, USA","institution_ids":["https://openalex.org/I127339705"]},{"raw_affiliation_string":"Department of Mathematics University of Kansas Lawrence, KS 66047 USA","institution_ids":["https://openalex.org/I146416000"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057471662"],"corresponding_institution_ids":["https://openalex.org/I127339705","https://openalex.org/I146416000"],"apc_list":null,"apc_paid":null,"fwci":0.96,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.73474515,"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/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/T11428","display_name":"Advanced Mathematical Identities","score":0.9957000017166138,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9955999851226807,"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/mathematics","display_name":"Mathematics","score":0.9062420129776001},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.7469092011451721},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.7307789325714111},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7185652852058411},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5658142566680908},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.4852454662322998},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4465585947036743},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4298231601715088},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.42948663234710693},{"id":"https://openalex.org/keywords/monomial-ideal","display_name":"Monomial ideal","score":0.42515045404434204},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3544219732284546},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12299373745918274},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.08733126521110535},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08580759167671204},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.07198980450630188},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.05075696110725403}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9062420129776001},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.7469092011451721},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.7307789325714111},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7185652852058411},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5658142566680908},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4852454662322998},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4465585947036743},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4298231601715088},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.42948663234710693},{"id":"https://openalex.org/C2777789435","wikidata":"https://www.wikidata.org/wiki/Q19369206","display_name":"Monomial ideal","level":4,"score":0.42515045404434204},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3544219732284546},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12299373745918274},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.08733126521110535},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08580759167671204},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.07198980450630188},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05075696110725403},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/171","is_oa":true,"landing_page_url":"https://doi.org/10.37236/171","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r82/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"}],"best_oa_location":{"id":"doi:10.37236/171","is_oa":true,"landing_page_url":"https://doi.org/10.37236/171","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r82/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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2157555182.pdf","grobid_xml":"https://content.openalex.org/works/W2157555182.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2008418827","https://openalex.org/W2126209209","https://openalex.org/W2168890963"],"related_works":["https://openalex.org/W2022115780","https://openalex.org/W1988302763","https://openalex.org/W2950419021","https://openalex.org/W4301463618","https://openalex.org/W2963131409","https://openalex.org/W3131141698","https://openalex.org/W4299339810","https://openalex.org/W1653027350","https://openalex.org/W4292635611","https://openalex.org/W2060971922"],"abstract_inverted_index":{"Let":[0],"$I_n$":[1,43,84],"be":[2],"the":[3,10,13,40,65,75,80],"ideal":[4,41,82],"of":[5,12,28,35,42,77,79,83],"all":[6],"algebraic":[7],"relations":[8],"on":[9],"slopes":[11],"${n\\choose2}$":[14],"lines":[15],"formed":[16],"by":[17,46,64],"placing":[18],"$n$":[19],"points":[20,29],"in":[21,85],"a":[22,31,52,72],"plane":[23],"and":[24],"connecting":[25],"each":[26,34,86],"pair":[27],"with":[30],"line.":[32],"Under":[33],"two":[36],"natural":[37],"term":[38],"orders,":[39],"is":[44],"generated":[45],"monomials":[47],"corresponding":[48],"to":[49],"permutations":[50,61],"satisfying":[51],"certain":[53],"pattern-avoidance":[54],"condition.":[55],"We":[56],"show":[57],"bijectively":[58],"that":[59],"these":[60],"are":[62],"enumerated":[63],"updown":[66],"(or":[67],"Euler)":[68],"numbers,":[69],"thereby":[70],"obtaining":[71],"formula":[73],"for":[74],"number":[76],"generators":[78],"initial":[81],"degree.":[87]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
