{"id":"https://openalex.org/W4414262455","doi":"https://doi.org/10.5070/c65365558","title":"The Newton polytope of the Kronecker product","display_name":"The Newton polytope of the Kronecker product","publication_year":2025,"publication_date":"2025-09-12","ids":{"openalex":"https://openalex.org/W4414262455","doi":"https://doi.org/10.5070/c65365558"},"language":"en","primary_location":{"id":"doi:10.5070/c65365558","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65365558","pdf_url":"https://escholarship.org/content/qt9dq590m9/qt9dq590m9.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://escholarship.org/content/qt9dq590m9/qt9dq590m9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049864711","display_name":"Greta Panova","orcid":"https://orcid.org/0000-0003-0785-1580"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Greta Panova","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100553857","display_name":"Chenchen Zhao","orcid":"https://orcid.org/0000-0001-8094-3591"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chenchen Zhao","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049864711"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.31716664,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9975000023841858,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9975000023841858,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9704999923706055,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9602000117301941,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/kronecker-product","display_name":"Kronecker product","score":0.7885000109672546},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6011000275611877},{"id":"https://openalex.org/keywords/kronecker-delta","display_name":"Kronecker delta","score":0.5993000268936157},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5860999822616577},{"id":"https://openalex.org/keywords/outer-product","display_name":"Outer product","score":0.4936999976634979},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.45890000462532043},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.44020000100135803},{"id":"https://openalex.org/keywords/birkhoff-polytope","display_name":"Birkhoff polytope","score":0.415800005197525}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8579000234603882},{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.7885000109672546},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6011000275611877},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.5993000268936157},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5860999822616577},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49950000643730164},{"id":"https://openalex.org/C180623205","wikidata":"https://www.wikidata.org/wiki/Q1268589","display_name":"Outer product","level":3,"score":0.4936999976634979},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.45890000462532043},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.44020000100135803},{"id":"https://openalex.org/C206304794","wikidata":"https://www.wikidata.org/wiki/Q4916482","display_name":"Birkhoff polytope","level":5,"score":0.415800005197525},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.39100000262260437},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3391000032424927},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33550000190734863},{"id":"https://openalex.org/C168310172","wikidata":"https://www.wikidata.org/wiki/Q493980","display_name":"Quiver","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C102591085","wikidata":"https://www.wikidata.org/wiki/Q17103152","display_name":"Schur product theorem","level":5,"score":0.3199999928474426},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3181999921798706},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.2612000107765198},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.2597000002861023},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5070/c65365558","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65365558","pdf_url":"https://escholarship.org/content/qt9dq590m9/qt9dq590m9.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},{"id":"pmh:doi:10.5070/C65365558","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S7407050878","display_name":"California Digital Library","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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/journal article"}],"best_oa_location":{"id":"doi:10.5070/c65365558","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65365558","pdf_url":"https://escholarship.org/content/qt9dq590m9/qt9dq590m9.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414262455.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,27],"study":[1],"the":[2,13,16,20,48,61],"Kronecker":[3,64,70],"product":[4,21],"of":[5,15,19,22,31,34,53,63],"two":[6,23],"Schur":[7],"functions":[8],"\\(s_\\lambda\\ast":[9],"s_\\mu\\),":[10],"defined":[11],"as":[12],"image":[14],"characteristic":[17],"map":[18],"\\(S_n\\)":[24],"irreducible":[25],"characters.":[26],"prove":[28],"special":[29],"cases":[30],"a":[32,41],"conjecture":[33],"Monical-Tokcan-Yong":[35],"that":[36],"its":[37],"monomial":[38],"expansion":[39],"has":[40],"saturated":[42,72],"Newton":[43,73],"polytope.":[44],"Our":[45],"proofs":[46],"employ":[47],"Horn":[49],"inequalities":[50],"for":[51,60],"positivity":[52,62],"Littlewood-Richardson":[54],"coefficients":[55],"and":[56],"imply":[57],"necessary":[58],"conditions":[59],"coefficients.Mathematics":[65],"Subject":[66],"Classifications:":[67],"05E10,":[68],"20C30Keywords:":[69],"coefficients,":[71],"polytope,":[74],"symmetric":[75],"group":[76],"representations":[77]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}
