Four generators of an equivalence lattice with consecutive block counts

2024/10/20 by Gábor Czédli, Czédli, Gábor
Computer Science · #06B99 #06C10 #Advanced Algebra and Logic #FOS: Mathematics #Rings and Algebras (math.RA) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2410.15328

openalex publication_date 2024/10/20 · openalex created_date 2024/11/06 · openalex updated_date 2026/07/28

Abstract

The block count of an equivalence μ∈ Equ(A) is the number blnum(μ) of blocks of (the partition corresponding to) μ. We say that X=\μ₁,μ₂,μ₃,μ₄\ is a four-element generating set of Equ(A) with consecutive block counts if X generates Equ(A) and blnum(μ_i+1) = blnum(μ₁)+i for i∈\1,2,3\. We prove that if the number of elements of a finite set A is six or at least eight, then Equ(A) has a four-element generating set with consecutive block counts. Also, we present a historical remark on the connection between equivalence lattices and quasiorder lattices.

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