{"id":"https://openalex.org/W4400720161","doi":"https://doi.org/10.48550/arxiv.2407.10927","title":"Puzzle Ideals for Grassmannians","display_name":"Puzzle Ideals for Grassmannians","publication_year":2024,"publication_date":"2024-07-15","ids":{"openalex":"https://openalex.org/W4400720161","doi":"https://doi.org/10.48550/arxiv.2407.10927"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2407.10927","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2407.10927","pdf_url":"https://arxiv.org/pdf/2407.10927","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2407.10927","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026125145","display_name":"Chenqi Mou","orcid":"https://orcid.org/0000-0002-5070-5928","observed_orcids":["https://orcid.org/0000-0002-5070-5928"]},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mou, Chenqi","raw_affiliation_strings":["LMIB -School of Mathematical Sciences , Beihang University , Beijing 100191 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMIB -School of Mathematical Sciences , Beihang University , Beijing 100191 , China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113292041","display_name":"Weifeng Shang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shang, Weifeng","raw_affiliation_strings":["LMIB -School of Mathematical Sciences , Beihang University , Beijing 100191 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMIB -School of Mathematical Sciences , Beihang University , Beijing 100191 , China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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":0.9932000041007996,"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":0.9932000041007996,"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":0.002400000113993883,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.0012000000569969416,"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/grassmannians","display_name":"Grassmannians","score":0.9229999780654907},{"id":"https://openalex.org/keywords/littlewood-richardson-coefficients","display_name":"Littlewood-Richardson coefficients","score":0.9890000224113464},{"id":"https://openalex.org/keywords/elimination-ideals","display_name":"elimination ideals","score":0.8270000219345093},{"id":"https://openalex.org/keywords/structure-constants","display_name":"structure constants","score":0.753000020980835},{"id":"https://openalex.org/keywords/grobner-bases","display_name":"Gr\u00f6bner bases","score":0.8550000190734863},{"id":"https://openalex.org/keywords/polynomial-systems","display_name":"polynomial systems","score":0.45100000500679016}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4073122441768646},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35790103673934937}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2407.10927","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2407.10927","pdf_url":"https://arxiv.org/pdf/2407.10927","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.2407.10927","doi":"https://doi.org/10.48550/arxiv.2407.10927","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2407.10927","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2407.10927","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2407.10927","pdf_url":"https://arxiv.org/pdf/2407.10927","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400720161.pdf","grobid_xml":"https://content.openalex.org/works/W4400720161.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Puzzles":[0],"are":[1],"a":[2],"versatile":[3],"combinatorial":[4],"tool":[5],"to":[6,27,37,74,101,121],"interpret":[7],"the":[8,18,28,39,45,66,75,81,85,91,94,102,106,111,118,124,127,133],"Littlewood-Richardson":[9],"coefficients":[10],"for":[11,54,58,97,129],"Grassmannians.":[12,55],"In":[13],"this":[14],"paper,":[15],"we":[16,64],"propose":[17,65],"concept":[19],"of":[20,30,77,84,93,110,113,126,143],"puzzle":[21,40,47,68,87,115],"ideals":[22,41,69,83,88,116],"whose":[23,70],"varieties":[24,71],"one-one":[25,72],"correspond":[26,73],"tilings":[29,76,125],"puzzles":[31,57,128,140],"and":[32,48,51,80],"present":[33],"an":[34],"algebraic":[35,108],"framework":[36],"construct":[38],"which":[42,59],"works":[43],"with":[44,99,138],"Knutson-Tao-Woodward":[46],"its":[49],"$T$-equivariant":[50],"$K$-theoretic":[52],"variants":[53],"For":[56],"one":[60],"side":[61],"is":[62,117],"free,":[63],"side-free":[67,78,86],"puzzles,":[79],"elimination":[82],"contain":[89],"all":[90,123],"information":[92],"structure":[95],"constants":[96],"Grassmannians":[98,130],"respect":[100],"free":[103],"side.":[104],"Besides":[105],"underlying":[107],"importance":[109],"introduction":[112],"these":[114],"computational":[119],"feasibility":[120],"find":[122],"by":[131],"solving":[132],"defining":[134],"polynomial":[135],"systems,":[136],"demonstrated":[137],"illustrative":[139],"via":[141],"computation":[142],"Gr\u00f6bner":[144],"bases.":[145]},"counts_by_year":[],"updated_date":"2026-09-30T09:27:27.532063","created_date":"2025-10-10T00:00:00"}