2018/09/19 by James E. East, Nik Ruškuc, East, James +1
Mathematics · Computer Science · #Advanced Mathematical Identities #Advanced Combinatorial Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1809.07427
We give a complete description of the congruences on the partition monoid PX and the partial Brauer monoid PBX, where X is an arbitrary infinite set, and also of the lattices formed by all such congruences. Our results complement those from a recent article of East, Mitchell, Ruskuc and Torpey, which deals with the finite case. As a consequence of our classification result, we show that the congruence lattices of PX and PBX are isomorphic to each other, and are distributive and well quasi-ordered. We also calculate the smallest number of pairs of partitions required to generate any congruence; when this number is infinite, it depends on the cofinality of certain limit cardinals.