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

dmtcs:3220 - Discrete Mathematics & Theoretical Computer Science, March 28, 2017, Vol 19 no. 1
S-Restricted Compositions Revisited

Authors: Zolfaghari, Behrouz and Fallah, Mehran S. and Sedighi, Mehdi

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.


Source : oai:arXiv.org:1606.07915
Volume: Vol 19 no. 1
Section: Combinatorics
Published on: March 28, 2017
Submitted on: March 28, 2017
Keywords: Mathematics - Combinatorics


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