Name
Abstract | ||
|---|---|---|
We investigate the numbers d(k) 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 v(k) of vertically indecomposable distributive lattices of size k. We present the explicit values of the numbers d(k) and v(k) for k < 50 and prove the following exponential bounds: 1.67(k) < v(k) < 2.33(k) and 1.84(k) < d(k) < 2.39(k) (k >= k(0)). Important tools are (i) an algorithm coding all unlabeled distributive lattices of height n and size k by certain integer sequences 0 = z(1) <= ... <= z(n) <= k - 2, and (ii) a "canonical 2 -decomposition" of ordinally indecomposable posets into "2-indecomposable" canonical summands. |
Year | Venue | Keywords |
|---|---|---|
2002 | ELECTRONIC JOURNAL OF COMBINATORICS | canonical poset,distributive lattice,ordinal (vertical) decomposition |
Field | DocType | Volume |
Discrete mathematics,Distributive property,Combinatorics,Distributive lattice,Lattice (order),Isomorphism,Indecomposable module,Mathematics | Journal | 9.0 |
Issue | ISSN | Citations |
1 | 1077-8926 | 8 |
PageRank | References | Authors |
1.59 | 2 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marcel Erné | 1 | 29 | 10.77 |
| Jobst Heitzig | 2 | 45 | 8.07 |
| Jürgen Reinhold | 3 | 31 | 5.89 |