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arxiv: 1801.01482 · v1 · pith:W3UGVP5Qnew · submitted 2018-01-04 · 🧮 math.RA · math.CO

Finite semilattices with many congruences

G\'abor Cz\'edli This is my paper
classification 🧮 math.RA math.CO
keywords ncslsemilatticeselementnumbersbelongingcongruencecongruencesdenote
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For an integer $n\geq 2$, 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$(n)|\geq 4$. Furthermore, we describe the $n$-element semilattices witnessing these numbers.

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  1. One hundred twenty-seven subsemilattices and planarity

    math.RA 2019-06 unverdicted novelty 6.0

    A finite n-element semilattice is planar if it has at least 127 * 2^(n-8) subsemilattices, and this bound is sharp for n > 8 via an explicit non-planar counterexample with one fewer subsemilattice.