Serial and Unserial Combinatorial Families

Abstract

This article presents the \emph{Serial and Unserial Methods} (SUM). The algorithms are strongly related to the first part of a classical reference in combinatorics, the \emph{Combinatorial algorithms for computers and calculators}, from Albert Nijenhuis and Herbert Wilf. The \emph{Serial Method} proposal is to obtain the output of a specific kind of combinatorial family from its position on the list of all combinatorial possibilities. The \emph{Unserial Method} is the inverted step of Serial Method, getting the serial number from the combinatorial family given as input. The \emph{serial number} is the position of the combinatorial family on the list.