On the Number of Distributive Lattices

@article{Ern2002OnTN,
  title={On the Number of Distributive Lattices},
  author={Marcel Ern{\'e} and Jobst Heitzig and J{\"u}rgen Reinhold},
  journal={Electr. J. Comb.},
  year={2002},
  volume={9}
}
We investigate the numbers dk of all (isomorphism classes of) distributive lattices with k elements, or, equivalently, of (unlabeled) posets with k antichains. Closely related and useful for combinatorial identities and inequalities are the numbers vk of vertically indecomposable distributive lattices of size k. We present the explicit values of the numbers dk and vk for k < 50 and prove the following exponential bounds: 1.67 < vk < 2.33 and 1.84 < dk < 2.39 (k > k0). Important tools are (i) an… CONTINUE READING

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