{"id":"https://openalex.org/W2062162600","doi":"https://doi.org/10.1137/0406042","title":"Monotone Optimal Multipartitions Using Schur Convexity with Respect to Partial Orders","display_name":"Monotone Optimal Multipartitions Using Schur Convexity with Respect to Partial Orders","publication_year":1993,"publication_date":"1993-11-01","ids":{"openalex":"https://openalex.org/W2062162600","doi":"https://doi.org/10.1137/0406042","mag":"2062162600"},"language":"en","primary_location":{"id":"doi:10.1137/0406042","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0406042","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103573008","display_name":"Frank K. Hwang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Frank K. Hwang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044612344","display_name":"Uriel G. Rothblum","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Uriel G. Rothblum","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5111774781","display_name":"L. A. Shepp","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Larry Shepp","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103573008"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3511,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.78116402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"6","issue":"4","first_page":"533","last_page":"547"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11502","display_name":"Facility Location and Emergency Management","score":0.9305999875068665,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9283000230789185,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.8511165380477905},{"id":"https://openalex.org/keywords/majorization","display_name":"Majorization","score":0.8469399213790894},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7715726494789124},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7099329829216003},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6930640935897827},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6829112768173218},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6104777455329895},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.6075536012649536},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.4843820035457611},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4695121943950653},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4670165181159973},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4539659917354584},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.4110540747642517},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07449564337730408}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8511165380477905},{"id":"https://openalex.org/C2777818330","wikidata":"https://www.wikidata.org/wiki/Q1994695","display_name":"Majorization","level":2,"score":0.8469399213790894},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7715726494789124},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7099329829216003},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6930640935897827},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6829112768173218},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6104777455329895},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6075536012649536},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.4843820035457611},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4695121943950653},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4670165181159973},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4539659917354584},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.4110540747642517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07449564337730408},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0406042","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0406042","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1973151204","https://openalex.org/W1991683408","https://openalex.org/W1993074922","https://openalex.org/W2035715326","https://openalex.org/W2039379871","https://openalex.org/W2059301258","https://openalex.org/W2075476714","https://openalex.org/W2085912217","https://openalex.org/W2111532899","https://openalex.org/W2137359697","https://openalex.org/W4300694379"],"related_works":["https://openalex.org/W2349952486","https://openalex.org/W1489260687","https://openalex.org/W2775700832","https://openalex.org/W2587222766","https://openalex.org/W3204670144","https://openalex.org/W2064678039","https://openalex.org/W2134933192","https://openalex.org/W2041678571","https://openalex.org/W2991798948","https://openalex.org/W2095532316"],"abstract_inverted_index":{"In":[0,77],"a":[1,85,90],"$(":[2,112],"t,n,m":[3],")$-multipartitioning":[4,114],"problem,":[5],"t":[6],"lists":[7],"of":[8,39,58,87,93],"$nm$":[9],"ordered":[10,67],"numbers":[11,22],"are":[12],"partitioned":[13],"into":[14],"n":[15],"sets,":[16],"where":[17],"each":[18,24,43],"set":[19,44],"contains":[20],"m":[21],"from":[23],"list.":[25],"The":[26,51],"goal":[27],"is":[28,46],"to":[29,65,69,83,89],"maximize":[30],"some":[31],"objective":[32],"function":[33],"that":[34,99],"depends":[35],"on":[36],"the":[37,40,48,54,74,81,108],"sum":[38],"elements":[41],"in":[42],"and":[45,60,95],"called":[47],"partition":[49,109],"function.":[50],"authors":[52],"use":[53],"recently":[55],"developed":[56],"theory":[57],"majorization":[59],"Schur":[61,101],"convexity":[62],"with":[63],"respect":[64],"partially":[66],"sets":[68],"study":[70],"optimal":[71,118],"multipartitions":[72],"for":[73,111],"above":[75],"problem.":[76],"particular,":[78],"they":[79],"apply":[80],"results":[82],"construct":[84],"class":[86],"counterexamples":[88],"recent":[91],"conjecture":[92],"Du":[94],"Hwang,":[96],"which":[97],"asserts":[98],"(classic)":[100],"convex":[102],"functions":[103,110],"can":[104],"be":[105],"characterized":[106],"as":[107],"1,n,m":[113],"problems":[115],"having":[116],"monotone":[117],"solutions.":[119]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}