Abstract
We show that there exist a set of polynomials { L k ⋎ k = 0, 1⋯} such that L k ( n) is the number of elements of rank k in the free distributive lattice on n generators. L 0( n) = L 1( n) = 1 for all n and the degree of L k is k−1 for k⩾1. We show that the coefficients of the L k can be calculated using another family of polynomials, P j . We show how to calculate L k for k = 1,…,16 and P j for j = 0,…,10. These calculations are enough to determine the number of elements of each rank in the free distributive lattice on 5 generators a result first obtained by Church [2]. We also calculate the asymptotic behavior of the L k 's and P j 's.
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