@inproceedings{2967af0b87634529bb53aaa8aad77384,
title = "Counting and Computing Join-Endomorphisms in Lattices",
abstract = "Structures involving a lattice and join-endomorphisms on it are ubiquitous in computer science. We study the cardinality of the set of all join-endomorphisms of a given finite lattice. In particular, we show that when is, the discrete order of n elements extended with top and bottom, where is the Laguerre polynomial of degree n. We also study the following problem: Given a lattice L of size n and a set of size m, find the greatest lower bound. The join-endomorphism has meaningful interpretations in epistemic logic, distributed systems, and Aumann structures. We show that this problem can be solved with worst-case time complexity in for powerset lattices, for lattices of sets, and for arbitrary lattices. The complexity is expressed in terms of the basic binary lattice operations performed by the algorithm.",
keywords = "Join-endomorphisms, Lattice algorithms, Lattice cardinality",
author = "Santiago Quintero and Sergio Ramirez and Camilo Rueda and Frank Valencia",
note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; 18th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2020 ; Conference date: 08-04-2020 Through 11-04-2020",
year = "2020",
month = jan,
day = "1",
doi = "10.1007/978-3-030-43520-2\_16",
language = "English",
isbn = "9783030435196",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer",
pages = "253--269",
editor = "Uli Fahrenberg and Peter Jipsen and Michael Winter",
booktitle = "Relational and Algebraic Methods in Computer Science - 18th International Conference, RAMiCS 2020, Proceedings",
}