
CHAPTER 5
Compositions and Decompositions
ABSTRACT
Compositions and decompositions for integers or for classes of objects are
studied using differential posets and dual graded graphs.
The relation with chemical engineering operations is highlighted.
Generating functions allows enumeration of species.
Entropy calculus is convenient to evaluate compositions versus
decomposition duality.
Keywords: circuit, composition, parallel, partition, Pascal graphs,
Schensted graphs, series
5.1 Compositions
5.1.1 Integers Composition
Composition in combinatorics is a rule specifying how two objects
pertaining to a combinatorial class can be combined to make another ...