relation: http://acta.bibl.u-szeged.hu/75848/
title: (1 + 1 + 2)-generated lattices of quasiorders
creator:  Ahmed Delbrin
creator:  Czédli Gábor
subject: 01. Természettudományok
subject: 01.01. Matematika
description: 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.
date: 2021
type: Cikk, tanulmány, mű
type: NonPeerReviewed
format: part
language: hu
identifier: http://acta.bibl.u-szeged.hu/75848/1/math_087_numb_003-004_415-427.pdf
identifier:    Ahmed Delbrin;  Czédli Gábor:   (1 + 1 + 2)-generated lattices of quasiorders.  In: Acta scientiarum mathematicarum, (87) 3-4.  pp. 415-427. (2021)   
language: eng