Yet Two Additional Large Numbers of Subuniverses of Finite Lattices

Delbrin Ahmed 1  and Eszter K. Horváth 1
  • 1 University of Szeged


By a subuniverse, we mean a sublattice or the emptyset. We prove that the fourth largest number of subuniverses of an n-element lattice is 43 2n−6 for n ≥ 6, and the fifth largest number of subuniverses of an n-element lattice is 85 2n−7 for n ≥ 7. Also, we describe the n-element lattices with exactly 43 2n−6 (for n ≥ 6) and 85 2n−7 (for n ≥ 7) subuniverses.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] G. Czédli, A note on finite lattices with many congruences, Acta Universitatis Matthiae Belii, Series Mathematics Online (2018) 22–28.

  • [2] G. Czédli, Lattices with many congruences are planar, Algebra Universalis (2019) 80:16. doi:10.1007/s00012-019-0589-1

  • [3] G. Czédli, Eighty-three sublattices and planarity.

  • [4] G. Czédli, Finite semilattices with many congruences, (Order). doi:10.1007/s11083-018-9464-5

  • [5] G. Czédli and E.K. Horváth, A note on lattices with many sublattices.

  • [6] G. Grätzer, Lattice Theory: Foundation (Birkhäuser Verlag, Basel, 2011). doi:10.1007/978-3-0348-0018-1

  • [7] I. Rival and R. Wille, Lattices freely generated by partially ordered sets: which can be “drawn”?, J. Reine Angew. Math. 310 (1979) 56–80. doi:10.1515/crll.1979.310.56


Journal + Issues