| Title:
|
Going down in (semi)lattices of finite Moore families and convex geometries (English) |
| Author:
|
Gabriela, Bordalo |
| Author:
|
Nathalie, Caspard |
| Author:
|
Bernard, Monjardet |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
249-271 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we first study what changes occur in the posets of irreducible elements when one goes from an arbitrary Moore family (respectively, a convex geometry) to one of its lower covers in the lattice of all Moore families (respectively, in the semilattice of all convex geometries) defined on a finite set. Then we study the set of all convex geometries which have the same poset of join-irreducible elements. We show that this set---ordered by set inclusion---is a ranked join-semilattice and we characterize its cover relation. We prove that the lattice of all ideals of a given poset $P$ is the only convex geometry having a poset of join-irreducible elements isomorphic to $P$ if and only if the width of $P$ is less than 3. Finally, we give an algorithm for computing all convex geometries having the same poset of join-irreducible elements. (English) |
| Keyword:
|
closure system |
| Keyword:
|
Moore family |
| Keyword:
|
convex geometry |
| Keyword:
|
(semi)lattice |
| Keyword:
|
algorithm |
| MSC:
|
06A12 |
| idZBL:
|
Zbl 1224.06005 |
| idMR:
|
MR2486629 |
| . |
| Date available:
|
2010-07-20T15:04:49Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140477 |
| . |
| Reference:
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