A graph-theoretic method to define any Boolean operation on partitions

Keywords: Set partitions, Boolean operations, graph-theoretic methods, closure-theoretic methods

Abstract

The lattice operations of join and meet were defined for set partitions in the nineteenth century, but no new logical operations on partitions were defined and studied during the twentieth century. Yet there is a simple and natural graph-theoretic method presented here to define any n-ary Boolean operation on partitions. An equivalent closure-theoretic method is also defined. In closing, the question is addressed of why it took so long for all Boolean operations to be defined for partitions.

Published
2019-06-10
Section
Non-Commutative Structures 2018