Behrouz Zolfaghari ; Mehran S. Fallah ; Mehdi Sedighi - S-Restricted Compositions Revisited

dmtcs:1522 - Discrete Mathematics & Theoretical Computer Science, March 28, 2017, Vol. 19 no. 1 -
S-Restricted Compositions RevisitedArticle

Authors: Behrouz Zolfaghari ORCID; Mehran S. Fallah ; Mehdi Sedighi

    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.

    Volume: Vol. 19 no. 1
    Section: Combinatorics
    Published on: March 28, 2017
    Accepted on: March 17, 2017
    Submitted on: March 28, 2017
    Keywords: Mathematics - Combinatorics

    Consultation statistics

    This page has been seen 548 times.
    This article's PDF has been downloaded 577 times.