Title

The Level Polynomials of the Free Distributive Lattices

Abstract

We show that there exist a set of polynomials {Lkk = 0, 1...} such that Lk(n) is the number of elements of rank k in the free distributive lattice on n generators. L0(n) = L1(n) = 1 for all n and the degree of Lk is k-1 for k⩾1. We show that the coefficients of the Lk can be calculated using another family of polynomials, Pj. We show how to calculate Lk for k = 1,...,16 and Pj 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 Lk's and Pj's.

Department(s)

Computer Science

International Standard Serial Number (ISSN)

0012-365X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1980 Elsevier, All rights reserved.

Share

 
COinS