Séminaire Lotharingien de Combinatoire, 93B.112 (2025), 12 pp.
Yongle Luo and Baptiste Rognerud
Lattice of Transfer Systems
Abstract.
We consider the lattice of all transfer systems on a given finite lattice L. We prove that it is semidistributive and as a corollary, we deduce a bijection between the transfer systems and the cliques of a graph whose vertices are the relations of L. As an application we find a lower bound for the number of transfer systems on a boolean lattice.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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