Journal article
S-Restricted Compositions Revisited
Discrete mathematics and theoretical computer science, Vol.19 (1), p.9
03/28/2017
Metrics
4 Record Views
Abstract
An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years. This paper is an attempt at finding a closed- form formula for the number of S-restricted compositions of n. To do so, we reduce the problem to finding solutions to corresponding so-called interpreters which are linear homogeneous recurrence relations with constant coefficients. Then, we reduce interpreters to Diophantine equations. Such equations are not in general solvable. Thus, we restrict our attention to those S-restricted composition problems whose interpreters have a small number of coefficients, thereby leading to solvable Diophantine equations. The formalism developed is then used to study the integer sequences related to some well-known cases of the S-restricted composition problem.
Files and links (2)
Related links
Details
- Title
- S-Restricted Compositions Revisited
- Publication Details
- Discrete mathematics and theoretical computer science, Vol.19 (1), p.9
- Resource Type
- Journal article
- Publisher
- D M T C S
- Copyright
- © 2017 by the author(s)
- Identifiers
- 99381506842106600
- Academic Unit
- Cybersecurity and Information Technology; Hal Marcus College of Science and Engineering
- Language
- English