1-Hypergroups of Small Sizes
In this paper, we show a new construction of hypergroups that, under appropriate conditions, are complete hypergroups or non-complete 1-hypergroups. Furthermore, we classify the 1-hypergroups of size 5 and 6 based on the partition induced by the fundamental relation <inline-formula><math di...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/2/108 |
| _version_ | 1797416065162018816 |
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| author | Mario De Salvo Dario Fasino Domenico Freni Giovanni Lo Faro |
| author_facet | Mario De Salvo Dario Fasino Domenico Freni Giovanni Lo Faro |
| author_sort | Mario De Salvo |
| collection | DOAJ |
| description | In this paper, we show a new construction of hypergroups that, under appropriate conditions, are complete hypergroups or non-complete 1-hypergroups. Furthermore, we classify the 1-hypergroups of size 5 and 6 based on the partition induced by the fundamental relation <inline-formula><math display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>. Many of these hypergroups can be obtained using the aforesaid hypergroup construction. |
| first_indexed | 2024-03-09T05:58:23Z |
| format | Article |
| id | doaj.art-7f632a33119c444f86a384db412c290a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:58:23Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7f632a33119c444f86a384db412c290a2023-12-03T12:11:22ZengMDPI AGMathematics2227-73902021-01-019210810.3390/math90201081-Hypergroups of Small SizesMario De Salvo0Dario Fasino1Domenico Freni2Giovanni Lo Faro3Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98122 Messina, ItalyDipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, 33100 Udine, ItalyDipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, 33100 Udine, ItalyDipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98122 Messina, ItalyIn this paper, we show a new construction of hypergroups that, under appropriate conditions, are complete hypergroups or non-complete 1-hypergroups. Furthermore, we classify the 1-hypergroups of size 5 and 6 based on the partition induced by the fundamental relation <inline-formula><math display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>. Many of these hypergroups can be obtained using the aforesaid hypergroup construction.https://www.mdpi.com/2227-7390/9/2/108hypergroupscomplete hypergroupsfundamental relations |
| spellingShingle | Mario De Salvo Dario Fasino Domenico Freni Giovanni Lo Faro 1-Hypergroups of Small Sizes Mathematics hypergroups complete hypergroups fundamental relations |
| title | 1-Hypergroups of Small Sizes |
| title_full | 1-Hypergroups of Small Sizes |
| title_fullStr | 1-Hypergroups of Small Sizes |
| title_full_unstemmed | 1-Hypergroups of Small Sizes |
| title_short | 1-Hypergroups of Small Sizes |
| title_sort | 1 hypergroups of small sizes |
| topic | hypergroups complete hypergroups fundamental relations |
| url | https://www.mdpi.com/2227-7390/9/2/108 |
| work_keys_str_mv | AT mariodesalvo 1hypergroupsofsmallsizes AT dariofasino 1hypergroupsofsmallsizes AT domenicofreni 1hypergroupsofsmallsizes AT giovannilofaro 1hypergroupsofsmallsizes |