Yet Two Additional Large Numbers of Subuniverses of Finite Lattices
By a subuniverse, we mean a sublattice or the emptyset. We prove that the fourth largest number of subuniverses of an n-element lattice is 43 2n−6 for n ≥ 6, and the fifth largest number of subuniverses of an n-element lattice is 85 2n−7 for n ≥ 7. Also, we describe the n-element lattices with exact...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2019-12-01
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| Series: | Discussiones Mathematicae - General Algebra and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgaa.1309 |
| _version_ | 1797723768739594240 |
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| author | Ahmed Delbrin Horváth Eszter K. |
| author_facet | Ahmed Delbrin Horváth Eszter K. |
| author_sort | Ahmed Delbrin |
| collection | DOAJ |
| description | By a subuniverse, we mean a sublattice or the emptyset. We prove that the fourth largest number of subuniverses of an n-element lattice is 43 2n−6 for n ≥ 6, and the fifth largest number of subuniverses of an n-element lattice is 85 2n−7 for n ≥ 7. Also, we describe the n-element lattices with exactly 43 2n−6 (for n ≥ 6) and 85 2n−7 (for n ≥ 7) subuniverses. |
| first_indexed | 2024-03-12T10:07:29Z |
| format | Article |
| id | doaj.art-85da2509617b476d9f37f6bddbdba2b8 |
| institution | Directory Open Access Journal |
| issn | 2084-0373 |
| language | English |
| last_indexed | 2024-03-12T10:07:29Z |
| publishDate | 2019-12-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae - General Algebra and Applications |
| spelling | doaj.art-85da2509617b476d9f37f6bddbdba2b82023-09-02T11:07:17ZengUniversity of Zielona GóraDiscussiones Mathematicae - General Algebra and Applications2084-03732019-12-0139225126110.7151/dmgaa.1309dmgaa.1309Yet Two Additional Large Numbers of Subuniverses of Finite LatticesAhmed Delbrin0Horváth Eszter K.1University of Szeged, Bolyai InstituteUniversity of Szeged, Bolyai InstituteBy a subuniverse, we mean a sublattice or the emptyset. We prove that the fourth largest number of subuniverses of an n-element lattice is 43 2n−6 for n ≥ 6, and the fifth largest number of subuniverses of an n-element lattice is 85 2n−7 for n ≥ 7. Also, we describe the n-element lattices with exactly 43 2n−6 (for n ≥ 6) and 85 2n−7 (for n ≥ 7) subuniverses.https://doi.org/10.7151/dmgaa.1309finite latticesublatticenumber of sublatticessubuniverseprimary: 06b99secondary: 08a30 |
| spellingShingle | Ahmed Delbrin Horváth Eszter K. Yet Two Additional Large Numbers of Subuniverses of Finite Lattices Discussiones Mathematicae - General Algebra and Applications finite lattice sublattice number of sublattices subuniverse primary: 06b99 secondary: 08a30 |
| title | Yet Two Additional Large Numbers of Subuniverses of Finite Lattices |
| title_full | Yet Two Additional Large Numbers of Subuniverses of Finite Lattices |
| title_fullStr | Yet Two Additional Large Numbers of Subuniverses of Finite Lattices |
| title_full_unstemmed | Yet Two Additional Large Numbers of Subuniverses of Finite Lattices |
| title_short | Yet Two Additional Large Numbers of Subuniverses of Finite Lattices |
| title_sort | yet two additional large numbers of subuniverses of finite lattices |
| topic | finite lattice sublattice number of sublattices subuniverse primary: 06b99 secondary: 08a30 |
| url | https://doi.org/10.7151/dmgaa.1309 |
| work_keys_str_mv | AT ahmeddelbrin yettwoadditionallargenumbersofsubuniversesoffinitelattices AT horvatheszterk yettwoadditionallargenumbersofsubuniversesoffinitelattices |