Enumeration Algorithms for Restricted and Unrestricted Compositions and Words

An overview of many of the major results in enumeration algorithms for Combinatorial Compositions can be found in this survey paper. The focus of this survey paper is on unrestricted compositions, bounded compositions, and future research in restricted compositions. The paper is concerned with generating these combinatorial objects, not counting the number of element under a composition. This paper includes a brief history of the problem, and theoretical connections found between combinatorial Gray-Codes, Integer Partitions, and common techniques established over the years. Lower-bound and upper-bound time and space complexities for these class of algorithms are covered where permitted. Primary focus will be given to sequential algorithms but in certain contexts concurrent and parallel solutions may be mentioned. The motivation is to further research in w-pattern avoidance and a generalized methods in enumerating restricted compositions and other formal languages.