(1 + 1 + 2)-generated lattices of quasiorders
A lattice is (1 + 1 + 2)-generated if it has a four-element generating set such that exactly two of the four generators are comparable. We prove that the lattice Quo(n) of all quasiorders (also known as preorders) of an n-element set is (1 + 1 + 2)-generated for n = 3 (trivially), n = 6 (when Quo(6)...
Elmentve itt :
| Szerzők: | |
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2021
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| Sorozat: | Acta scientiarum mathematicarum
87 No. 3-4 |
| Kulcsszavak: | Matematika, Algebra |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-021-303-1 |
| Online Access: | http://acta.bibl.u-szeged.hu/75848 |
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| 024 | 7 | |a 10.14232/actasm-021-303-1 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Ahmed Delbrin | |
| 245 | 1 | 0 | |a (1 + 1 + 2)-generated lattices of quasiorders |h [elektronikus dokumentum] / |c Ahmed Delbrin |
| 260 | |c 2021 | ||
| 300 | |a 415-427 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 87 No. 3-4 | |
| 520 | 3 | |a A lattice is (1 + 1 + 2)-generated if it has a four-element generating set such that exactly two of the four generators are comparable. We prove that the lattice Quo(n) of all quasiorders (also known as preorders) of an n-element set is (1 + 1 + 2)-generated for n = 3 (trivially), n = 6 (when Quo(6) consists of 209 527 elements), n = 11, and for every natural number n ≥ 13. In 2017, the second author and J. Kulin proved that Quo(n) is (1 + 1 + 2)-generated if either n is odd and at least 13 or n is even and at least 56. Compared to the 2017 result, this paper presents twenty-four new numbers n such that Quo(n) is (1 + 1 + 2)-generated. Except for Quo(6), an extension of Zádori’s method is used. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Matematika | |
| 695 | |a Matematika, Algebra | ||
| 700 | 0 | 1 | |a Czédli Gábor |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/75848/1/math_087_numb_003-004_415-427.pdf |z Dokumentum-elérés |