David Ellerman: A graph-theoretic algorithm to define any Boolean operation on set partitions

Date of publication: 17. 9. 2018
Mathematics and theoretical computing seminar
Četrtek, 20. 9. 2018, od 11h do 13h, učilnica 3.07, Jadranska 21
Phil. Dept., University of California at Riverside,
School of Social Sciences, University of Ljubljana, Slovenia 

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 given. In closing, the question is addressed of why it took so long for all Boolean operations to be defined for partitions so that the logic of partitions could be developed as the dual to the Boolean logic of subsets. [Paper forthcoming in the Slovene journal, Art of Discrete and Applied Mathematics (ADAM)].