10.23638/DMTCS-19-1-9
https://dmtcs.episciences.org/1522
Zolfaghari, Behrouz
Behrouz
Zolfaghari
Fallah, Mehran S.
Mehran S.
Fallah
Sedighi, Mehdi
Mehdi
Sedighi
S-Restricted Compositions Revisited
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.
episciences.org
Mathematics - Combinatorics
2017-03-28
2017-03-28
2017-03-28
eng
journal article
arXiv:1606.07915
10.48550/arXiv.1606.07915
1365-8050
https://dmtcs.episciences.org/1522/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
Vol. 19 no. 1
Combinatorics
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