8 - Combinatorial and quantum techniques for large data sets: hypercubes and halocarbons

Abstract

We present an overview of combinatorial techniques for studying large data sets with hypercubes and halocarbons as the foci. We outline a variety of combinatorial techniques such as the Möbius inversion and generalization of Sheehan’s enumerative combinatorics for all characters for the equivalence classes for coloring hyperplanes of hypercubes with a given set of color partitions. The techniques are also applicable to the enumeration of stereo and position isomers of polysubstituted halocarbons. Hypercubes are of considerable interest in large data sets such as genetic regulatory networks, potential energy surfaces of molecules, and visualizations. Halocarbons are of interest because they are environmental pollutants and due to their potential toxicity including carcinogenicity. The combinatorial techniques have the capability not only to generate a large data set to provide a platform for further analysis but also to obtain structure–property relations. Furthermore, quantum chemical techniques provide electronic parameters that are of potential use in the toxicity predictions of a large dataset of halocarbons. In particular, the quantum parameters for the Crebellei data set of 55 halocarbons are reviewed to enhance our understanding of the mode toxicity action of these compounds.