Orderly Majority Functions with their Relation to Minimal Clones
Hajime Machida · 2024
For majority functions on finite sets, we define the concepts of orderly and doubly orderly and prove the following. For a 2-valued (on triples with mutually distinct components) majority function$f$, the clone generated by$f$always contains an orderly majority function. With an additional assumption imposed on some values of$f$, the clone generated by$f$contains a doubly orderly majority function. Based on these observations, we present a new class of minimal functions.