The number of slim rectangular lattices
Slim rectangular lattices are special planar semimodular lattices introduced by G. Grätzer and E. Knapp in 2009. They are finite semimodular lattices L such that the ordered set Ji L of join-irreducible elements of L is the cardinal sum of two nontrivial chains. After describing these lattices of a...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2016
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| Sorozat: | ALGEBRA UNIVERSALIS
75 No. 1 |
| doi: | 10.1007/s00012-015-0363-y |
| mtmt: | 2987391 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/14520 |
| Tartalmi kivonat: | Slim rectangular lattices are special planar semimodular lattices introduced by G. Grätzer and E. Knapp in 2009. They are finite semimodular lattices L such that the ordered set Ji L of join-irreducible elements of L is the cardinal sum of two nontrivial chains. After describing these lattices of a given length n by permutations, we determine their number, |SRectL(n)|. Besides giving recursive formulas, which are effective up to about n = 1000, we also prove that |SRectL(n)| is asymptotically (n - 2)! · (Formula presented.). Similar results for patch lattices, which are special rectangular lattices introduced by G. Czédli and E. T. Schmidt in 2013, and for slim rectangular lattice diagrams are also given. © 2015 Springer International Publishing |
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| Terjedelem/Fizikai jellemzők: | 33-50 |
| ISSN: | 0002-5240 |