{"id":"https://openalex.org/W7203704082","doi":"https://doi.org/10.48550/arxiv.2608.14985","title":"A polynomial time algorithm for almost bounded denumerant","display_name":"A polynomial time algorithm for almost bounded denumerant","publication_year":2026,"publication_date":"2026-08-15","ids":{"openalex":"https://openalex.org/W7203704082","doi":"https://doi.org/10.48550/arxiv.2608.14985"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.14985","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.14985","pdf_url":"https://arxiv.org/pdf/2608.14985","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.14985","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049446116","display_name":"Guoce Xin","orcid":"https://orcid.org/0000-0002-2505-5759","observed_orcids":["https://orcid.org/0000-0002-2505-5759","https://orcid.org/0000-0001-6259-1385"]},"institutions":[{"id":"https://openalex.org/I96852419","display_name":"Capital Normal University","ror":"https://ror.org/005edt527","country_code":"CN","type":"education","lineage":["https://openalex.org/I96852419"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin, Guoce","raw_affiliation_strings":["School of Mathematical Sciences , Capital Normal University , Beijing , 100048 , PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Capital Normal University , Beijing , 100048 , PR China","institution_ids":["https://openalex.org/I96852419"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5147400748","display_name":"Chen Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Chen","raw_affiliation_strings":["Center for Combinatorics , LPMC , Nankai University , Tianjin 300071 , PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Combinatorics , LPMC , Nankai University , Tianjin 300071 , PR China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5143461054","display_name":"Zihao Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Zihao","raw_affiliation_strings":["School of Mathematics and Statistics , Beijing Institute of Technology , Beijing 102400 , PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Beijing Institute of Technology , Beijing 102400 , PR China","institution_ids":["https://openalex.org/I125839683"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":0.9463000297546387,"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":0.9463000297546387,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.04010000079870224,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.0038999998942017555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polynomial-time-algorithms","display_name":"polynomial-time algorithms","score":0.7250000238418579},{"id":"https://openalex.org/keywords/bounded-coefficients","display_name":"bounded coefficients","score":0.5410000085830688},{"id":"https://openalex.org/keywords/unbounded-coefficients","display_name":"unbounded coefficients","score":0.8679999709129333},{"id":"https://openalex.org/keywords/lattice-point-counting","display_name":"lattice point counting","score":0.4830000102519989},{"id":"https://openalex.org/keywords/coin-change-problem","display_name":"coin change problem","score":0.3869999945163727}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7304999828338623},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6855999827384949},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.6187000274658203},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6029999852180481},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5490999817848206},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.541700005531311},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5414000153541565},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5383999943733215},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4332999885082245},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.31839999556541443},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.29820001125335693},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.29190000891685486},{"id":"https://openalex.org/C2778751112","wikidata":"https://www.wikidata.org/wiki/Q835016","display_name":"Window (computing)","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.26649999618530273},{"id":"https://openalex.org/C2777045944","wikidata":"https://www.wikidata.org/wiki/Q12170198","display_name":"Zh\u00e0ng","level":3,"score":0.2533000111579895},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.14985","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.14985","pdf_url":"https://arxiv.org/pdf/2608.14985","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.2608.14985","doi":"https://doi.org/10.48550/arxiv.2608.14985","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.14985","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.14985","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.14985","pdf_url":"https://arxiv.org/pdf/2608.14985","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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G7799225896","display_name":null,"funder_award_id":"12571355","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203704082.pdf","grobid_xml":"https://content.openalex.org/works/W7203704082.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4411986028","https://openalex.org/W4407391676","https://openalex.org/W2952805049","https://openalex.org/W4409919131","https://openalex.org/W2602263550","https://openalex.org/W7095923682","https://openalex.org/W7168274741","https://openalex.org/W4225163185","https://openalex.org/W7124436325","https://openalex.org/W4404939876"],"abstract_inverted_index":{"Sylvester's":[0],"denumerant":[1],"$d(t;":[2,47],"\\boldsymbol{A})$":[3,48],"counts":[4],"the":[5,50,74],"number":[6,79],"of":[7,26,52,80,82],"nonnegative":[8],"integer":[9],"solutions":[10],"to":[11,72,86],"$\\sum_{i=1}^{N}":[12],"a_i":[13],"x_i":[14],"=":[15,19,31],"t$,":[16],"where":[17,76],"$\\boldsymbol{A}":[18],"(a_1,":[20],"\\dots,":[21],"a_N)$":[22],"is":[23],"a":[24,39,57,77],"sequence":[25],"positive":[27],"integers":[28],"with":[29],"$\\gcd(\\boldsymbol{A})":[30],"1$.":[32],"In":[33,59],"2025,":[34],"Xin":[35],"and":[36],"Zhang":[37],"gave":[38],"polynomial":[40],"time":[41],"algorithm":[42,65],"in":[43],"$N$":[44],"for":[45],"computing":[46],"when":[49],"entries":[51,81],"$\\boldsymbol{A}$":[53,83],"are":[54,84],"bounded":[55],"by":[56,66],"constant.":[58],"this":[60,64],"paper,":[61],"we":[62],"extend":[63],"incorporating":[67],"Barvinok's":[68],"algorithm,":[69],"enabling":[70],"it":[71],"handle":[73],"case":[75],"fixed":[78],"allowed":[85],"be":[87],"unbounded.":[88]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-19T00:00:00"}