Similarity and dissimilarity in posets

摘要

The relevance of partially ordered sets (or posets) in a wide diversity of contexts in chemistry is emphasized, and the utility of distance functions (or metrics) on such posets is noted. First a notion of "scale similarity" is introduced to make comparisons within certain so-called "scaled" posets, for which there is formulated natural "comparators", which in turn lead to associated distance functions. Beyond taking note of several chemically relevant examples of these "scaled" posets and their consequent associated similarity measures, a second chemically relevant class of so-called "shifted" posets is similarly developed, with examples. Even further extension of some aspects of the current approach is indicated, and finally the multi-posetic character of chemical periodic law is suggested.