학술논문
The number of subuniverses, congruences, weak congruences of semilattices defined by trees.
Document Type
Journal
Author
Ahmed, Delbrin (H-SZEG-B) AMS Author Profile; Horváth, Eszter K. (H-SZEG-ANT) AMS Author Profile; Németh, Zoltán (H-SZEG-AN) AMS Author Profile
Source
Subject
05 Combinatorics -- 05A Enumerative combinatorics
05A15Exact enumeration problems, generating functions
05Combinatorics -- 05C Graph theory
05C05Trees
06Order, lattices, ordered algebraic structures -- 06A Ordered sets
06A12Semilattices
08General algebraic systems -- 08A Algebraic structures
08A30Subalgebras, congruence relations
05A15
05
05C05
06
06A12
08
08A30
Language
English
Abstract
In this paper, the authors determine the number of subuniverses of semilattices defined by arbitrary and special kinds of trees via combinatorial considerations. They also give a formula for the number of congruences of semilattices defined by arbitrary and special kinds of trees by using a result of Freese and Nation. Using both results, they prove a formula for the number of weak congruences of semilattices defined by a binary tree, and discuss some special cases. Finally, they solve two apparently nontrivial recurrences by applying the method of Aho and Sloane.