{"id":"https://openalex.org/W7208704247","doi":"https://doi.org/10.48550/arxiv.2609.02932","title":"Enumerating Chemical Structures, Stereoisomers, and Stereogenic Units with Analytic Combinatorics","display_name":"Enumerating Chemical Structures, Stereoisomers, and Stereogenic Units with Analytic Combinatorics","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7208704247","doi":"https://doi.org/10.48550/arxiv.2609.02932"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.02932","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02932","pdf_url":"https://arxiv.org/pdf/2609.02932","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/2609.02932","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102791490","display_name":"Casper Asbj\u00f8rn Eriksen","orcid":"https://orcid.org/0000-0003-0474-9468","observed_orcids":["https://orcid.org/0000-0003-0474-9468"]},"institutions":[{"id":"https://openalex.org/I177969490","display_name":"University of Southern Denmark","ror":"https://ror.org/03yrrjy16","country_code":"DK","type":"education","lineage":["https://openalex.org/I177969490"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Eriksen, Casper Asbj\u00f8rn","raw_affiliation_strings":["Department of Mathematics and Computer Science , University of Southern Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science , University of Southern Denmark","institution_ids":["https://openalex.org/I177969490"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5149522632","display_name":"Daniel Merkle","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Merkle, Daniel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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":0.9028000235557556,"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":0.9028000235557556,"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/T12527","display_name":"Chemistry and Stereochemistry Studies","score":0.05000000074505806,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.028599999845027924,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stereoisomers","display_name":"stereoisomers","score":0.7590000033378601},{"id":"https://openalex.org/keywords/analytic-combinatorics","display_name":"analytic combinatorics","score":0.8949999809265137},{"id":"https://openalex.org/keywords/symbolic-methods","display_name":"symbolic methods","score":0.9850000143051147},{"id":"https://openalex.org/keywords/hydrocarbons","display_name":"hydrocarbons","score":0.9070000052452087},{"id":"https://openalex.org/keywords/e-z-isomerism","display_name":"E/Z isomerism","score":0.7979999780654907},{"id":"https://openalex.org/keywords/meso-compounds","display_name":"meso compounds","score":0.9340000152587891},{"id":"https://openalex.org/keywords/achiral-compounds","display_name":"achiral compounds","score":0.9490000009536743},{"id":"https://openalex.org/keywords/generating-functions","display_name":"generating functions","score":0.765999972820282}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.8747000098228455},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5475000143051147},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5156999826431274},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.5092999935150146},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5080000162124634},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44519999623298645},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42489999532699585},{"id":"https://openalex.org/C44210515","wikidata":"https://www.wikidata.org/wiki/Q16968978","display_name":"Bespoke","level":2,"score":0.36660000681877136},{"id":"https://openalex.org/C2987825933","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorial analysis","level":2,"score":0.365200012922287},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.3610000014305115},{"id":"https://openalex.org/C154485487","wikidata":"https://www.wikidata.org/wiki/Q815666","display_name":"Bell polynomials","level":2,"score":0.3587000072002411},{"id":"https://openalex.org/C2284495","wikidata":"https://www.wikidata.org/wiki/Q2601117","display_name":"Stirling numbers of the second kind","level":2,"score":0.3449000120162964},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3379000127315521},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32670000195503235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32120001316070557},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.3158999979496002},{"id":"https://openalex.org/C115908005","wikidata":"https://www.wikidata.org/wiki/Q2668364","display_name":"Combinatorial explosion","level":2,"score":0.3095000088214874},{"id":"https://openalex.org/C16592021","wikidata":"https://www.wikidata.org/wiki/Q5177154","display_name":"Counting problem","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.2906999886035919},{"id":"https://openalex.org/C2776372474","wikidata":"https://www.wikidata.org/wiki/Q508291","display_name":"Simplicity","level":2,"score":0.2897000014781952},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2549000084400177}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.02932","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02932","pdf_url":"https://arxiv.org/pdf/2609.02932","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.02932","doi":"https://doi.org/10.48550/arxiv.2609.02932","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.02932","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.02932","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02932","pdf_url":"https://arxiv.org/pdf/2609.02932","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G2942398999","display_name":null,"funder_award_id":"NNF21OC0066551","funder_id":"https://openalex.org/F4320322436","funder_display_name":"Novo Nordisk"},{"id":"https://openalex.org/G6894179864","display_name":null,"funder_award_id":"NNF19OC0057834","funder_id":"https://openalex.org/F4320322436","funder_display_name":"Novo Nordisk"}],"funders":[{"id":"https://openalex.org/F4320322436","display_name":"Novo Nordisk","ror":"https://ror.org/0435rc536"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7208704247.pdf","grobid_xml":"https://content.openalex.org/works/W7208704247.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2098195816"],"related_works":["https://openalex.org/W2952833805","https://openalex.org/W1983038754","https://openalex.org/W4317695442","https://openalex.org/W2068237573","https://openalex.org/W2057956901","https://openalex.org/W4256034358","https://openalex.org/W2083404468","https://openalex.org/W1884460706","https://openalex.org/W3119388630","https://openalex.org/W2092183901"],"abstract_inverted_index":{"The":[0],"enumeration":[1,61,76],"of":[2,33,77,92,95,102,131,143,167],"chemical":[3],"structures":[4],"traditionally":[5],"relies":[6],"on":[7],"graph-":[8],"and":[9,27,35,56,80,119,137,146,149,177,181],"group-theoretic":[10],"techniques,":[11],"including":[12],"P\u00f3lya":[13],"theory,":[14],"in":[15,109],"order":[16],"to":[17,124],"account":[18],"for":[19,29,40,60,134],"stereochemical":[20],"symmetries.":[21],"These":[22],"methods":[23,28],"require":[24],"bespoke":[25],"derivations":[26],"each":[30],"molecular":[31],"family":[32],"interest,":[34],"quickly":[36],"become":[37],"very":[38],"intricate":[39],"nontrivial":[41],"classes.":[42],"In":[43],"this":[44,103,110],"work,":[45],"we":[46,67],"demonstrate":[47,99],"that":[48,69],"analytic":[49],"combinatorics":[50],"provides":[51],"a":[52],"unifying,":[53],"highly":[54],"extensible,":[55],"relatively":[57],"simple":[58],"framework":[59],"problems.":[62],"Using":[63],"the":[64,75,93,100,141,165,174],"symbolic":[65,175],"method,":[66,176],"show":[68],"classical":[70],"counting":[71,128,140],"problems,":[72,127],"such":[73],"as":[74],"acyclic":[78],"alkanes":[79],"other":[81],"hydrocarbon":[82],"families,":[83],"can":[84],"be":[85],"naturally":[86],"solved":[87],"via":[88],"concise":[89],"combinatorial":[90,168],"specifications":[91,169],"class":[94],"interest.":[96],"We":[97],"first":[98],"simplicity":[101],"approach":[104],"by":[105],"replicating":[106],"existing":[107],"results":[108,153],"framework,":[111],"requiring":[112],"significantly":[113],"less":[114],"work":[115],"than":[116],"previously":[117],"necessary,":[118],"then":[120],"extend":[121],"these":[122],"ideas":[123],"more":[125],"complex":[126],"broader":[129],"classes":[130],"molecules":[132],"accounting":[133],"both":[135,179],"tetrahedral":[136],"E/Z":[138],"stereoisomerism,":[139],"distribution":[142],"stereogenic":[144],"units,":[145],"enumerating":[147],"achiral":[148],"meso":[150],"compounds.":[151],"All":[152],"are":[154],"made":[155],"reproducible":[156],"through":[157],"CombOL,":[158],"our":[159],"open-source":[160],"software":[161],"package":[162],"which":[163],"automates":[164],"translation":[166],"into":[170],"generating":[171],"functions":[172],"using":[173],"performs":[178],"univariate":[180],"multivariate":[182],"enumeration.":[183]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-05T00:00:00"}
