A concise approach to small generating sets of lattices of quasiorders and transitive relations

2016/09/05 by Czédli, Gábor, Kulin, Júlia
#06B99 #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1609.01016

Abstract

By H. Strietz, 1975, and G. Czédli, 1996, the complete lattice Equ(A) of all equivalences is four-generated, provided the size |A| is an accessible cardinal. Results of I. Chajda and G. Czédli, 1996, G. Takách, 1996, T. Dolgos, 2015, and J. Kulin 2016, show that both the lattice Quo(A) of all quasiorders on A and, for |A|≤ ℵ₀, the lattice Tran(A) of all transitive relations on A have small generating sets. Based on complicated earlier constructions, we derive some new results in a concise but not self-contained way.

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