Counting Compositions over Finite Abelian Groups Article Swipe
Zhicheng Gao
,
Andrew MacFie
,
Qiang Wang
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.37236/7591
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.37236/7591
We find the number of compositions over finite abelian groups under two types of restrictions: (i) each part belongs to a given subset and (ii) small runs of consecutive parts must have given properties. Waring's problem over finite fields can be converted to type (i) compositions, whereas Carlitz and "locally Mullen" compositions can be formulated as type (ii) compositions. We use the multisection formula to translate the problem from integers to group elements, the transfer matrix method to do exact counting, and finally the Perron-Frobenius theorem to derive asymptotics. We also exhibit bijections involving certain restricted classes of compositions.
Related Topics
Concepts
Mathematics
Bijection, injection and surjection
Abelian group
Type (biology)
Combinatorics
Finite field
Group (periodic table)
Matrix (chemical analysis)
Transfer (computing)
Discrete mathematics
Pure mathematics
Bijection
Chemistry
Computer science
Composite material
Biology
Organic chemistry
Parallel computing
Ecology
Materials science
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.37236/7591
- OA Status
- diamond
- Cited By
- 5
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2963047229
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W2963047229Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.37236/7591Digital Object Identifier
- Title
-
Counting Compositions over Finite Abelian GroupsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2018Year of publication
- Publication date
-
2018-04-27Full publication date if available
- Authors
-
Zhicheng Gao, Andrew MacFie, Qiang WangList of authors in order
- Landing page
-
https://doi.org/10.37236/7591Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
diamondOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.37236/7591Direct OA link when available
- Concepts
-
Mathematics, Bijection, injection and surjection, Abelian group, Type (biology), Combinatorics, Finite field, Group (periodic table), Matrix (chemical analysis), Transfer (computing), Discrete mathematics, Pure mathematics, Bijection, Chemistry, Computer science, Composite material, Biology, Organic chemistry, Parallel computing, Ecology, Materials scienceTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
5Total citation count in OpenAlex
- Citations by year (recent)
-
2022: 1, 2021: 2, 2019: 2Per-year citation counts (last 5 years)
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W2963047229 |
|---|---|
| doi | https://doi.org/10.37236/7591 |
| ids.doi | https://doi.org/10.37236/7591 |
| ids.mag | 2963047229 |
| ids.openalex | https://openalex.org/W2963047229 |
| fwci | 0.42841845 |
| type | article |
| title | Counting Compositions over Finite Abelian Groups |
| biblio.issue | 2 |
| biblio.volume | 25 |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T12029 |
| topics[0].field.id | https://openalex.org/fields/13 |
| topics[0].field.display_name | Biochemistry, Genetics and Molecular Biology |
| topics[0].score | 0.9969000220298767 |
| topics[0].domain.id | https://openalex.org/domains/1 |
| topics[0].domain.display_name | Life Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1312 |
| topics[0].subfield.display_name | Molecular Biology |
| topics[0].display_name | DNA and Biological Computing |
| topics[1].id | https://openalex.org/T11567 |
| topics[1].field.id | https://openalex.org/fields/17 |
| topics[1].field.display_name | Computer Science |
| topics[1].score | 0.9962999820709229 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/1703 |
| topics[1].subfield.display_name | Computational Theory and Mathematics |
| topics[1].display_name | semigroups and automata theory |
| topics[2].id | https://openalex.org/T11476 |
| topics[2].field.id | https://openalex.org/fields/26 |
| topics[2].field.display_name | Mathematics |
| topics[2].score | 0.9932000041007996 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2608 |
| topics[2].subfield.display_name | Geometry and Topology |
| topics[2].display_name | Graph theory and applications |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C33923547 |
| concepts[0].level | 0 |
| concepts[0].score | 0.9240162372589111 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[0].display_name | Mathematics |
| concepts[1].id | https://openalex.org/C48659774 |
| concepts[1].level | 3 |
| concepts[1].score | 0.8458194732666016 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q4907197 |
| concepts[1].display_name | Bijection, injection and surjection |
| concepts[2].id | https://openalex.org/C136170076 |
| concepts[2].level | 2 |
| concepts[2].score | 0.7994970679283142 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q181296 |
| concepts[2].display_name | Abelian group |
| concepts[3].id | https://openalex.org/C2777299769 |
| concepts[3].level | 2 |
| concepts[3].score | 0.6065735816955566 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q3707858 |
| concepts[3].display_name | Type (biology) |
| concepts[4].id | https://openalex.org/C114614502 |
| concepts[4].level | 1 |
| concepts[4].score | 0.5686532258987427 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q76592 |
| concepts[4].display_name | Combinatorics |
| concepts[5].id | https://openalex.org/C77926391 |
| concepts[5].level | 2 |
| concepts[5].score | 0.5263962745666504 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q603880 |
| concepts[5].display_name | Finite field |
| concepts[6].id | https://openalex.org/C2781311116 |
| concepts[6].level | 2 |
| concepts[6].score | 0.49825525283813477 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q83306 |
| concepts[6].display_name | Group (periodic table) |
| concepts[7].id | https://openalex.org/C106487976 |
| concepts[7].level | 2 |
| concepts[7].score | 0.4690556824207306 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q685816 |
| concepts[7].display_name | Matrix (chemical analysis) |
| concepts[8].id | https://openalex.org/C2776175482 |
| concepts[8].level | 2 |
| concepts[8].score | 0.44326338171958923 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q1195816 |
| concepts[8].display_name | Transfer (computing) |
| concepts[9].id | https://openalex.org/C118615104 |
| concepts[9].level | 1 |
| concepts[9].score | 0.39428091049194336 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q121416 |
| concepts[9].display_name | Discrete mathematics |
| concepts[10].id | https://openalex.org/C202444582 |
| concepts[10].level | 1 |
| concepts[10].score | 0.33597224950790405 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q837863 |
| concepts[10].display_name | Pure mathematics |
| concepts[11].id | https://openalex.org/C24424167 |
| concepts[11].level | 2 |
| concepts[11].score | 0.13420522212982178 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q180907 |
| concepts[11].display_name | Bijection |
| concepts[12].id | https://openalex.org/C185592680 |
| concepts[12].level | 0 |
| concepts[12].score | 0.0 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q2329 |
| concepts[12].display_name | Chemistry |
| concepts[13].id | https://openalex.org/C41008148 |
| concepts[13].level | 0 |
| concepts[13].score | 0.0 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[13].display_name | Computer science |
| concepts[14].id | https://openalex.org/C159985019 |
| concepts[14].level | 1 |
| concepts[14].score | 0.0 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q181790 |
| concepts[14].display_name | Composite material |
| concepts[15].id | https://openalex.org/C86803240 |
| concepts[15].level | 0 |
| concepts[15].score | 0.0 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q420 |
| concepts[15].display_name | Biology |
| concepts[16].id | https://openalex.org/C178790620 |
| concepts[16].level | 1 |
| concepts[16].score | 0.0 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q11351 |
| concepts[16].display_name | Organic chemistry |
| concepts[17].id | https://openalex.org/C173608175 |
| concepts[17].level | 1 |
| concepts[17].score | 0.0 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q232661 |
| concepts[17].display_name | Parallel computing |
| concepts[18].id | https://openalex.org/C18903297 |
| concepts[18].level | 1 |
| concepts[18].score | 0.0 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q7150 |
| concepts[18].display_name | Ecology |
| concepts[19].id | https://openalex.org/C192562407 |
| concepts[19].level | 0 |
| concepts[19].score | 0.0 |
| concepts[19].wikidata | https://www.wikidata.org/wiki/Q228736 |
| concepts[19].display_name | Materials science |
| keywords[0].id | https://openalex.org/keywords/mathematics |
| keywords[0].score | 0.9240162372589111 |
| keywords[0].display_name | Mathematics |
| keywords[1].id | https://openalex.org/keywords/bijection-injection-and-surjection |
| keywords[1].score | 0.8458194732666016 |
| keywords[1].display_name | Bijection, injection and surjection |
| keywords[2].id | https://openalex.org/keywords/abelian-group |
| keywords[2].score | 0.7994970679283142 |
| keywords[2].display_name | Abelian group |
| keywords[3].id | https://openalex.org/keywords/type |
| keywords[3].score | 0.6065735816955566 |
| keywords[3].display_name | Type (biology) |
| keywords[4].id | https://openalex.org/keywords/combinatorics |
| keywords[4].score | 0.5686532258987427 |
| keywords[4].display_name | Combinatorics |
| keywords[5].id | https://openalex.org/keywords/finite-field |
| keywords[5].score | 0.5263962745666504 |
| keywords[5].display_name | Finite field |
| keywords[6].id | https://openalex.org/keywords/group |
| keywords[6].score | 0.49825525283813477 |
| keywords[6].display_name | Group (periodic table) |
| keywords[7].id | https://openalex.org/keywords/matrix |
| keywords[7].score | 0.4690556824207306 |
| keywords[7].display_name | Matrix (chemical analysis) |
| keywords[8].id | https://openalex.org/keywords/transfer |
| keywords[8].score | 0.44326338171958923 |
| keywords[8].display_name | Transfer (computing) |
| keywords[9].id | https://openalex.org/keywords/discrete-mathematics |
| keywords[9].score | 0.39428091049194336 |
| keywords[9].display_name | Discrete mathematics |
| keywords[10].id | https://openalex.org/keywords/pure-mathematics |
| keywords[10].score | 0.33597224950790405 |
| keywords[10].display_name | Pure mathematics |
| keywords[11].id | https://openalex.org/keywords/bijection |
| keywords[11].score | 0.13420522212982178 |
| keywords[11].display_name | Bijection |
| language | en |
| locations[0].id | doi:10.37236/7591 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S38448739 |
| locations[0].source.issn | 1077-8926, 1097-1440 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | 1077-8926 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | True |
| locations[0].source.display_name | The Electronic Journal of Combinatorics |
| locations[0].source.host_organization | https://openalex.org/P4310317970 |
| locations[0].source.host_organization_name | Electronic Journal of Combinatorics |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310317970 |
| locations[0].license | cc-by |
| locations[0].pdf_url | |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | The Electronic Journal of Combinatorics |
| locations[0].landing_page_url | https://doi.org/10.37236/7591 |
| indexed_in | crossref, doaj |
| authorships[0].author.id | https://openalex.org/A5102714122 |
| authorships[0].author.orcid | https://orcid.org/0000-0001-6488-8721 |
| authorships[0].author.display_name | Zhicheng Gao |
| authorships[0].countries | CA |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I67031392 |
| authorships[0].affiliations[0].raw_affiliation_string | Carleton University |
| authorships[0].institutions[0].id | https://openalex.org/I67031392 |
| authorships[0].institutions[0].ror | https://ror.org/02qtvee93 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I67031392 |
| authorships[0].institutions[0].country_code | CA |
| authorships[0].institutions[0].display_name | Carleton University |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Zhicheng Gao |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | Carleton University |
| authorships[1].author.id | https://openalex.org/A5060564223 |
| authorships[1].author.orcid | |
| authorships[1].author.display_name | Andrew MacFie |
| authorships[1].countries | CA |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I67031392 |
| authorships[1].affiliations[0].raw_affiliation_string | Carleton University |
| authorships[1].institutions[0].id | https://openalex.org/I67031392 |
| authorships[1].institutions[0].ror | https://ror.org/02qtvee93 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I67031392 |
| authorships[1].institutions[0].country_code | CA |
| authorships[1].institutions[0].display_name | Carleton University |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Andrew MacFie |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Carleton University |
| authorships[2].author.id | https://openalex.org/A5100366899 |
| authorships[2].author.orcid | https://orcid.org/0000-0001-5426-2776 |
| authorships[2].author.display_name | Qiang Wang |
| authorships[2].countries | CA |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I67031392 |
| authorships[2].affiliations[0].raw_affiliation_string | Carleton University |
| authorships[2].institutions[0].id | https://openalex.org/I67031392 |
| authorships[2].institutions[0].ror | https://ror.org/02qtvee93 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I67031392 |
| authorships[2].institutions[0].country_code | CA |
| authorships[2].institutions[0].display_name | Carleton University |
| authorships[2].author_position | last |
| authorships[2].raw_author_name | Qiang Wang |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | Carleton University |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://doi.org/10.37236/7591 |
| open_access.oa_status | diamond |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Counting Compositions over Finite Abelian Groups |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T12029 |
| primary_topic.field.id | https://openalex.org/fields/13 |
| primary_topic.field.display_name | Biochemistry, Genetics and Molecular Biology |
| primary_topic.score | 0.9969000220298767 |
| primary_topic.domain.id | https://openalex.org/domains/1 |
| primary_topic.domain.display_name | Life Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1312 |
| primary_topic.subfield.display_name | Molecular Biology |
| primary_topic.display_name | DNA and Biological Computing |
| related_works | https://openalex.org/W1991467510, https://openalex.org/W2952277453, https://openalex.org/W2952259524, https://openalex.org/W4286233230, https://openalex.org/W1669060173, https://openalex.org/W2160566290, https://openalex.org/W1986815418, https://openalex.org/W2922282992, https://openalex.org/W4299839951, https://openalex.org/W2951615080 |
| cited_by_count | 5 |
| counts_by_year[0].year | 2022 |
| counts_by_year[0].cited_by_count | 1 |
| counts_by_year[1].year | 2021 |
| counts_by_year[1].cited_by_count | 2 |
| counts_by_year[2].year | 2019 |
| counts_by_year[2].cited_by_count | 2 |
| locations_count | 1 |
| best_oa_location.id | doi:10.37236/7591 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S38448739 |
| best_oa_location.source.issn | 1077-8926, 1097-1440 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | 1077-8926 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | True |
| best_oa_location.source.display_name | The Electronic Journal of Combinatorics |
| best_oa_location.source.host_organization | https://openalex.org/P4310317970 |
| best_oa_location.source.host_organization_name | Electronic Journal of Combinatorics |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310317970 |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | The Electronic Journal of Combinatorics |
| best_oa_location.landing_page_url | https://doi.org/10.37236/7591 |
| primary_location.id | doi:10.37236/7591 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S38448739 |
| primary_location.source.issn | 1077-8926, 1097-1440 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | 1077-8926 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | True |
| primary_location.source.display_name | The Electronic Journal of Combinatorics |
| primary_location.source.host_organization | https://openalex.org/P4310317970 |
| primary_location.source.host_organization_name | Electronic Journal of Combinatorics |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310317970 |
| primary_location.license | cc-by |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | The Electronic Journal of Combinatorics |
| primary_location.landing_page_url | https://doi.org/10.37236/7591 |
| publication_date | 2018-04-27 |
| publication_year | 2018 |
| referenced_works_count | 0 |
| abstract_inverted_index.a | 20 |
| abstract_inverted_index.We | 0, 59, 89 |
| abstract_inverted_index.as | 55 |
| abstract_inverted_index.be | 40, 53 |
| abstract_inverted_index.do | 78 |
| abstract_inverted_index.of | 4, 13, 27, 97 |
| abstract_inverted_index.to | 19, 42, 64, 70, 77, 86 |
| abstract_inverted_index.(i) | 15, 44 |
| abstract_inverted_index.and | 23, 48, 81 |
| abstract_inverted_index.can | 39, 52 |
| abstract_inverted_index.the | 2, 61, 66, 73, 83 |
| abstract_inverted_index.two | 11 |
| abstract_inverted_index.use | 60 |
| abstract_inverted_index.(ii) | 24, 57 |
| abstract_inverted_index.also | 90 |
| abstract_inverted_index.each | 16 |
| abstract_inverted_index.find | 1 |
| abstract_inverted_index.from | 68 |
| abstract_inverted_index.have | 31 |
| abstract_inverted_index.must | 30 |
| abstract_inverted_index.over | 6, 36 |
| abstract_inverted_index.part | 17 |
| abstract_inverted_index.runs | 26 |
| abstract_inverted_index.type | 43, 56 |
| abstract_inverted_index.exact | 79 |
| abstract_inverted_index.given | 21, 32 |
| abstract_inverted_index.group | 71 |
| abstract_inverted_index.parts | 29 |
| abstract_inverted_index.small | 25 |
| abstract_inverted_index.types | 12 |
| abstract_inverted_index.under | 10 |
| abstract_inverted_index.derive | 87 |
| abstract_inverted_index.fields | 38 |
| abstract_inverted_index.finite | 7, 37 |
| abstract_inverted_index.groups | 9 |
| abstract_inverted_index.matrix | 75 |
| abstract_inverted_index.method | 76 |
| abstract_inverted_index.number | 3 |
| abstract_inverted_index.subset | 22 |
| abstract_inverted_index.Carlitz | 47 |
| abstract_inverted_index.Mullen" | 50 |
| abstract_inverted_index.abelian | 8 |
| abstract_inverted_index.belongs | 18 |
| abstract_inverted_index.certain | 94 |
| abstract_inverted_index.classes | 96 |
| abstract_inverted_index.exhibit | 91 |
| abstract_inverted_index.finally | 82 |
| abstract_inverted_index.formula | 63 |
| abstract_inverted_index.problem | 35, 67 |
| abstract_inverted_index.theorem | 85 |
| abstract_inverted_index.whereas | 46 |
| abstract_inverted_index."locally | 49 |
| abstract_inverted_index.Waring's | 34 |
| abstract_inverted_index.integers | 69 |
| abstract_inverted_index.transfer | 74 |
| abstract_inverted_index.converted | 41 |
| abstract_inverted_index.counting, | 80 |
| abstract_inverted_index.elements, | 72 |
| abstract_inverted_index.involving | 93 |
| abstract_inverted_index.translate | 65 |
| abstract_inverted_index.bijections | 92 |
| abstract_inverted_index.formulated | 54 |
| abstract_inverted_index.restricted | 95 |
| abstract_inverted_index.consecutive | 28 |
| abstract_inverted_index.properties. | 33 |
| abstract_inverted_index.asymptotics. | 88 |
| abstract_inverted_index.compositions | 5, 51 |
| abstract_inverted_index.multisection | 62 |
| abstract_inverted_index.compositions, | 45 |
| abstract_inverted_index.compositions. | 58, 98 |
| abstract_inverted_index.restrictions: | 14 |
| abstract_inverted_index.Perron-Frobenius | 84 |
| cited_by_percentile_year.max | 96 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.61999853 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |