(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: | |
|---|---|
| Dokumentumtípus: | Cikk |
| Megjelent: |
2021
|
| 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 |
| Tartalmi kivonat: | 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. |
|---|---|
| Terjedelem/Fizikai jellemzők: | 415-427 |
| ISSN: | 2064-8316 |