On the lattice of tolerances for a finite chain

Górnicka, A.; Grygiel, Joanna; Tyrala, Iwona

doi:10.16926/m.2016.21.03

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2018

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“…The present paper is primarily motivated by a problem on tolerance relations of lattices raised by Joanna Grygiel in her conference talk in September, 2017, which was a continuation of Górnicka, Grygiel, and Tyrala [5]. Further motivation is supplied by Czédli [1], Czédli and Mureşan [2], Kulin and Mureşan [8], and Mureşan [9], still dealing with lattices rather than semilattices.…”

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confidence: 99%

Finite Semilattices with Many Congruences

Czédli

2018

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For an integer n ≥ 2, let NCSL(n) denote the set of sizes of congruence lattices of n-element semilattices. We find the four largest numbers belonging to NCSL(n), provided that n is large enough to ensure that |NCSL(n)| ≥ 4. Furthermore, we describe the n-element semilattices witnessing these numbers.1991 Mathematics Subject Classification. 06A12, secondary 06B10 January 4, 2018. Key words and phrases. Number of lattice congruences, size of the congruence lattice of a finite lattice, lattice with many congruences.

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Section: Introductionmentioning

confidence: 99%

Finite Semilattices with Many Congruences

Czédli

2018

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On the lattice of tolerances for a finite chain

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Finite Semilattices with Many Congruences

Finite Semilattices with Many Congruences

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