Combinatorics

Abstract

The formal study of combinatorics dates at least to Gottfried Wilhelm Leibniz’s Dissertatio de Arte Combinatoria in the seventeenth century. The last half-century, however, has seen a huge growth in the subject, fueled by problems and applications from many fields of study. Applications of combinatorics arise, for example, in chemistry, in studying arrangements of atoms in molecules and crystals; biology, in questions about the structure of genes and proteins; physics, in problems in statistical mechanics; communications, in the design of codes for encryption, compression, and correction of errors; and especially computer science, for instance in problems of scheduling and allocating resources and in analyzing the efficiency of algorithms.

[Combinatorics] has emerged as a new subject standing at the crossroads between pure and applied mathematics the center of bustling activity, a simmering pot of new problems and exciting speculations.

— Gian-Carlo Rota, [129, p. vii]