Papers › Counting graded lattices of rank three that have few coatoms
Counting graded lattices of rank three that have few coatoms
Jukka Kohonen
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We consider the problem of computing R(c,a), the number of unlabeled graded lattices of rank 3 that contain c coatoms and a atoms. More specifically we do this when c is fairly small, but a may be large. For this task, we describe a computational method that combines constructive listing of basic cases and tools from enumerative combinatorics. With this method we compute the exact values of R(c,a) for c≤9 and a≤1000. We also show that, for any fixed c, there exists a quasipolynomial in a that matches with R(c,a) for all a above a small value. We explicitly determine these quasipolynomials for c ≤7, thus finding closed form expressions of R(c,a) for c ≤7.
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