Leírás
This is a joint work with Delbrin Ahmed (first part) and Andreja Tepavcevic
(second part). In the first part of the talk, the number of subuniverses of
semilattices defined by arbitrary and special kinds of trees will be
given via combinatorial considerations. Using a result of Freese and
Nation, we give a formula for the number of congruences of
semilattices defined by arbitrary and special kinds of trees, as well
as some interesting properties of the congruence lattice of a
semilattice corresponding to a tree. Using the number of subuniverses
and the number of congruences, we will give a formula for the number
of weak congruences of semilattices defined by a binary tree. Some
special cases will be discussed. The solution of two apparently
nontrivial recurrences will be presented.
In the second part of the talk, we determine the two greatest numbers
of weak congruences of lattices. The number of weak congruences of
some special lattices, such as lanterns (on a chain) and chandeliers,
will be deduced via combinatorial considerations.