episciences.org_1522_1664546369
1664546369
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
13658050
03
28
2017
Vol. 19 no. 1
Combinatorics
SRestricted Compositions Revisited
Behrouz
Zolfaghari
Mehran S.
Fallah
Mehdi
Sedighi
An Srestricted 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 Srestricted compositions of n. To do so, we reduce
the problem to finding solutions to corresponding socalled 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 Srestricted
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 wellknown cases of
the Srestricted composition problem.
03
28
2017
1522
arXiv:1606.07915
10.48550/arXiv.1606.07915
https://arxiv.org/abs/1606.07915v2
https://arxiv.org/abs/1606.07915v1
10.23638/DMTCS1919
https://dmtcs.episciences.org/1522

https://dmtcs.episciences.org/3220/pdf