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Group2: Generating the Finest Partition that is Coarser than Two Given Partitions

In this article, I develop a useful interpretation of the function group() based on partitions belonging to mathematical set theory, an interpretation that in turn engenders a related command here called group2. In the context of the partitioning of sets, while the function group() creates a variable that generates the coarsest partition that is finer than the finest partition generated by the variables used as arguments, the group2 command will create a variable that generates the finest partition that is coarser than the coarsest partition generated by the variables used as arguments. This latter operation has proven very useful in several problems of database management. An introduction of this new command in the context of mathematical partitions is provided, and two examples of its application are presented.