{"id":"https://openalex.org/W2067308203","doi":"https://doi.org/10.1137/s0895480198349014","title":"Partitions and (<i>m</i> and <i>n</i>) Sums of Products---Two Cell Partition","display_name":"Partitions and (<i>m</i> and <i>n</i>) Sums of Products---Two Cell Partition","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2067308203","doi":"https://doi.org/10.1137/s0895480198349014","mag":"2067308203"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480198349014","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480198349014","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/A5006338528","display_name":"Gregory L. Smith","orcid":"https://orcid.org/0000-0002-1985-2882"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gregory L. Smith","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006338528"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2131015,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"3","first_page":"356","last_page":"369"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9980000257492065,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9980000257492065,"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/T14500","display_name":"Advanced Mathematical Theories","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9923999905586243,"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/partition","display_name":"Partition (number theory)","score":0.7976476550102234},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7951728105545044},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6729096174240112},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4362800419330597}],"concepts":[{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.7976476550102234},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7951728105545044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6729096174240112},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4362800419330597},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895480198349014","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480198349014","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":2,"referenced_works":["https://openalex.org/W1987346952","https://openalex.org/W2023397165"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"We":[0],"let":[1],"$SP_m":[2],"(\\langle":[3,42],"X_t":[4,17,50],"\\rangle^\\infty_{t=1})$":[5],"denote":[6],"the":[7],"sums":[8],"of":[9,29],"m":[10],"increasing":[11],"products":[12],"from":[13],"a":[14,25],"sequence":[15],"$\\langle":[16,49,53],"\\rangle^{\\infty}_{t=1}$.":[18],"Given":[19],"$m":[20],"\\neq":[21],"n$,":[22],"we":[23],"construct":[24],"two":[26],"cell":[27,34],"partition":[28],"$\\mathbb{N}$":[30],"so":[31],"that":[32],"neither":[33],"contains":[35],"$SP_n":[36],"\\langle":[37],"X":[38],"\\rangle^{\\infty}_{t=1})":[39],"\\cup":[40],"SP_m":[41],"y\\rangle>^{\\infty}_{t":[43],"=":[44],"1})$":[45],"for":[46],"any":[47],"sequences":[48],"\\rangle^{\\infty}_{t=1}$":[51],"and":[52],"y":[54],"\\rangle^\\infty_{t=1}$.":[55]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
