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The level polynomials of the free distributive lattices

โœ Scribed by George Markowsky

Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
915 KB
Volume
29
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

We show that there exist a set of polynomials {Lk 1 k = 0, 1 * * a} such that L,(n) is the number of elements of rank k in the free distributive lattice on n generators. L,(n) = L,(n) = 1 for all n and the degree of L, is k -1 for k 5 1. We show that the coefficients of the L, can be calculated using another family of polynomials, Pi. We show how to calculate L, for k = 1 **, 16 and Pi for j=O,..., 10. These calculations are enough to determine the number of eie'ments 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,'s and Pj'S.

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