Some Extremal Values of the Number of Congruences of a Finite Lattice

2018/01/16 by Júlia Kulin, Kulin, J\' ulia, Claudia Mureșan +1
Computer Science · Mathematics · #06B05 #06B10 #Advanced Algebra and Logic #Advanced Mathematical Identities #FOS: Mathematics #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.1801.05282

openalex publication_date 2018/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the smallest, as well as the largest numbers of congruences of lattices of an arbitrary finite cardinality n. Continuing the work of Freese and Cz' edli, we prove that the third, fourth and fifth largest numbers of congruences of an n--element lattice are: 5⋅ 2^n-5 if n≥ 5, respectively 2^n-3 and 7⋅ 2^n-6 if n≥ 6. We also determine the structures of the n--element lattices having 5⋅ 2^n-5, respectively 2^n-3 congruences, along with the structures of their congruence lattices.

Citations

• A note on finite lattices with many congruences

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