{"id":"https://openalex.org/W2056025450","doi":"https://doi.org/10.1007/s00454-004-1131-5","title":"The Partial-Fractions Method for Counting Solutions to Integral Linear Systems","display_name":"The Partial-Fractions Method for Counting Solutions to Integral Linear Systems","publication_year":2004,"publication_date":"2004-09-06","ids":{"openalex":"https://openalex.org/W2056025450","doi":"https://doi.org/10.1007/s00454-004-1131-5","mag":"2056025450"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-004-1131-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-004-1131-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1131-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1131-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101449510","display_name":"Matthias Beck","orcid":"https://orcid.org/0000-0001-8889-785X"},"institutions":[{"id":"https://openalex.org/I71838634","display_name":"San Francisco State University","ror":"https://ror.org/05ykr0121","country_code":"US","type":"education","lineage":["https://openalex.org/I71838634"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matthias Beck","raw_affiliation_strings":["Department of Mathematics, San Francisco State University, 1600 Holloway Avenue, San\nFrancisco, CA 94132, USA","Department of Mathematics, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, San Francisco State University, 1600 Holloway Avenue, San\nFrancisco, CA 94132, USA","institution_ids":["https://openalex.org/I71838634"]},{"raw_affiliation_string":"Department of Mathematics, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA","institution_ids":["https://openalex.org/I71838634"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101449510"],"corresponding_institution_ids":["https://openalex.org/I71838634"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":4.6765,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.93670886,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"32","issue":"4","first_page":"437","last_page":"446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9997000098228455,"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":0.9997000098228455,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9904000163078308,"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":0.8372814059257507},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.7592604160308838},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7080730199813843},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6822283267974854},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5777705907821655},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5240935683250427},{"id":"https://openalex.org/keywords/partition-function","display_name":"Partition function (quantum field theory)","score":0.47467494010925293},{"id":"https://openalex.org/keywords/partial-fraction-decomposition","display_name":"Partial fraction decomposition","score":0.4322744905948639},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43021538853645325},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.41451945900917053},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33051931858062744},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18916583061218262},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.06821763515472412},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05260235071182251}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8372814059257507},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7592604160308838},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7080730199813843},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6822283267974854},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5777705907821655},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5240935683250427},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.47467494010925293},{"id":"https://openalex.org/C66103642","wikidata":"https://www.wikidata.org/wiki/Q431617","display_name":"Partial fraction decomposition","level":3,"score":0.4322744905948639},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43021538853645325},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.41451945900917053},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33051931858062744},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18916583061218262},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.06821763515472412},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05260235071182251},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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":6,"locations":[{"id":"doi:10.1007/s00454-004-1131-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-004-1131-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1131-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.236.7758","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.7758","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0309332v3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.237.3566","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.237.3566","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0309332v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.237.3764","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.237.3764","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0309332v2.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:233818","is_oa":false,"landing_page_url":"http://edoc.mpg.de/233818","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"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":"Discrete &amp; Computational Geometry, v.32, 437-446 (2004)","raw_type":"Article"},{"id":"pmh:oai:pure.mpg.de:item_3124649","is_oa":false,"landing_page_url":"http://hdl.handle.net/21.11116/0000-0004-3016-D","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete & Computational Geometry","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00454-004-1131-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-004-1131-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1131-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2056025450.pdf","grobid_xml":"https://content.openalex.org/works/W2056025450.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W20523863","https://openalex.org/W1482232916","https://openalex.org/W1508632565","https://openalex.org/W1528466706","https://openalex.org/W1597196612","https://openalex.org/W1640396639","https://openalex.org/W1971718614","https://openalex.org/W1979041943","https://openalex.org/W2008119321","https://openalex.org/W2033084216","https://openalex.org/W2059237901","https://openalex.org/W2064897100","https://openalex.org/W2072364436","https://openalex.org/W2074744502","https://openalex.org/W2077818624","https://openalex.org/W2085110259","https://openalex.org/W2118938101","https://openalex.org/W2129740858","https://openalex.org/W2169157953","https://openalex.org/W2952189129","https://openalex.org/W2953162326","https://openalex.org/W3186607004","https://openalex.org/W4251668311","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4280529077","https://openalex.org/W2507185596","https://openalex.org/W1493684871","https://openalex.org/W4286224459","https://openalex.org/W2886567582","https://openalex.org/W4289703404","https://openalex.org/W4387265813","https://openalex.org/W3103454236","https://openalex.org/W4294567731","https://openalex.org/W2808407214"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-09T07:27:16.801131","created_date":"2025-10-10T00:00:00"}
