Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1-23 |
| Seitenumfang | 23 |
| Fachzeitschrift | Electronic Journal of Combinatorics |
| Jahrgang | 9 |
| Ausgabenummer | 1 R |
| Publikationsstatus | Veröffentlicht - 1 Apr. 2002 |
Abstract
We investigate the numbers dk 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 vk of vertically indecomposable distributive lattices of size k. We present the explicit values of the numbers dk and vk for k < 50 and prove the following exponential bounds: 1.67k < vk lt; 2.33k and 1.84k < dk < 2.39k (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 = z1 ≤ ⋯ ≤ zn ≤ k - 2, and (ii) a "canonical 2-decomposition" of ordinally indecomposable posets into "2-indecomposable" canonical summands.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Theoretische Informatik
- Mathematik (insg.)
- Geometrie und Topologie
- Mathematik (insg.)
- Diskrete Mathematik und Kombinatorik
- Informatik (insg.)
- Theoretische Informatik und Mathematik
- Mathematik (insg.)
- Angewandte Mathematik
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in: Electronic Journal of Combinatorics, Jahrgang 9, Nr. 1 R, 01.04.2002, S. 1-23.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - On the number of distributive lattices
AU - Ernë, Marcel
AU - Heitzig, Jobst
AU - Reinhold, Jürgen
PY - 2002/4/1
Y1 - 2002/4/1
N2 - We investigate the numbers dk 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 vk of vertically indecomposable distributive lattices of size k. We present the explicit values of the numbers dk and vk for k < 50 and prove the following exponential bounds: 1.67k < vk lt; 2.33k and 1.84k < dk < 2.39k (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 = z1 ≤ ⋯ ≤ zn ≤ k - 2, and (ii) a "canonical 2-decomposition" of ordinally indecomposable posets into "2-indecomposable" canonical summands.
AB - We investigate the numbers dk 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 vk of vertically indecomposable distributive lattices of size k. We present the explicit values of the numbers dk and vk for k < 50 and prove the following exponential bounds: 1.67k < vk lt; 2.33k and 1.84k < dk < 2.39k (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 = z1 ≤ ⋯ ≤ zn ≤ k - 2, and (ii) a "canonical 2-decomposition" of ordinally indecomposable posets into "2-indecomposable" canonical summands.
KW - Canonical poset
KW - Distributive lattice
KW - Ordinal (vertical) decomposition
UR - http://www.scopus.com/inward/record.url?scp=4043176865&partnerID=8YFLogxK
U2 - 10.37236/1641
DO - 10.37236/1641
M3 - Article
AN - SCOPUS:4043176865
VL - 9
SP - 1
EP - 23
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
SN - 1077-8926
IS - 1 R
ER -