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math.CO2020
Cartesian lattice counting by the vertical 2-sum
Jukka Kohonen
A vertical 2-sum of a two-coatom lattice and a two-atom lattice is obtained by removing the top of and the bottom of , and identifying the coatoms of with the at…
math.CO2018
Counting graded lattices of rank three that have few coatoms
Jukka Kohonen
We consider the problem of computing , the number of unlabeled graded lattices of rank that contain coatoms and atoms. More specifically we do this when is…
math.CO2018
Exponential lower bounds of lattice counts by vertical sum and 2-sum
Jukka Kohonen
We consider the problem of finding lower bounds on the number of unlabeled -element lattices in some lattice family. We show that if the family is closed under vertical sum, exp…