(1 + 1 + 2)generated lattices of quasiorders
A lattice is (1 + 1 + 2)generated if it has a fourelement 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 nelement set is (1 + 1 + 2)generated for n = 3 (trivially), n = 6 (when Quo(6)...
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Format:  Article 
Published: 
2021

Series:  Acta scientiarum mathematicarum
87 No. 34 
Kulcsszavak:  Matematika, Algebra 
Subjects:  
doi:  10.14232/actasm0213031 
Online Access:  http://acta.bibl.uszeged.hu/75848 
Summary:  A lattice is (1 + 1 + 2)generated if it has a fourelement 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 nelement 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 twentyfour new numbers n such that Quo(n) is (1 + 1 + 2)generated. Except for Quo(6), an extension of Zádori’s method is used. 

Physical Description:  415427 
ISSN:  20648316 