A solution of Dedekind's problem on the number of isotone Boolean functions.

  title={A solution of Dedekind's problem on the number of isotone Boolean functions.},
  author={Andrzej P. Kisielewicz},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  pages={139 - 144}
  • A. Kisielewicz
  • Published 1988
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
Almost one hundred years ago R. Dedekind raised the problem to determine the number D (n) of elements in the free bounded distributive lattice on n generators which is the same s the number of isotone maps from the Boolean lattice T into 2. D (n) is also the number of antichains in 2 and also the number of simplicial complexes on n elements (cf. [4], [9], [20], [21]). The problem was considered by many authors, but so far only partial results were obtained: asymptotic estimations [12], [13… 
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