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- W4289542409 abstract "We give a complete description of the congruences on the partition monoid $P_X$ and the partial Brauer monoid $PB_X$, 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 $P_X$ and $PB_X$ 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." @default.
- W4289542409 created "2022-08-03" @default.
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- W4289542409 date "2018-09-19" @default.
- W4289542409 modified "2023-09-26" @default.
- W4289542409 title "Congruences on infinite partition and partial Brauer monoids" @default.
- W4289542409 doi "https://doi.org/10.48550/arxiv.1809.07427" @default.
- W4289542409 hasPublicationYear "2018" @default.
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