English

On the lattice of the weak factorization systems on a finite lattice

Combinatorics 2024-10-10 v1 Algebraic Topology Group Theory Representation Theory

Abstract

We consider the lattice of all the weak factorization systems on a given finite lattice. We prove that it is semidistributive, trim and congruence uniform. We deduce a graph theoretical approach to the problem of enumerating transfer systems. As an application we find a lower bound for the number of transfer systems on a boolean lattice.

Keywords

Cite

@article{arxiv.2410.06182,
  title  = {On the lattice of the weak factorization systems on a finite lattice},
  author = {Yongle Luo and Baptiste Rognerud},
  journal= {arXiv preprint arXiv:2410.06182},
  year   = {2024}
}

Comments

49 pages, comments are welcome