A general formula in composition theory
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Rafael Jakimczuk
Abstract
We prove general formulae in composition theory. We study the number of restricted compositions of a positive integer n in k parts, where the parts are in very general integer sequences. Note that in compositions the order of the parts is considered.
Acknowledgement
The author is very grateful to the anonymous reviewers for their helpful suggestions and to Professor Djamel Bellaouar from University 08 Mai 45 Guelma for his help in the preparation of the final files. The author is very grateful to Universidad Nacional de Luján.
Communicated by István Gaál
References
[1] Jha, S. K.: An identity for the sum of inverses of odd divisors of n in terms of the number of representations of n as sum of squares, Rocky Mountain J. Math. 51(2) (2021), 581–583.10.1216/rmj.2021.51.581Search in Google Scholar
[2] Lam-Estrada, P.—López-Bonilla, J.: On the Jha’s identity for the sum of inverses of odd divisors of a positive integer, Comput. Appl. Math. Soc. 6(2) (2021), 27–29.Search in Google Scholar
[3] Nathanson, M. B.: Additive Number Theory, Springer, New York, 1996.10.1007/978-1-4757-3845-2Search in Google Scholar
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Articles in the same Issue
- On the Paley graph of a quadratic character
- A topological duality for tense modal pseudocomplemented De Morgan algebras
- Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers
- A general formula in composition theory
- A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity
- On universality in short intervals for zeta-functions of certain cusp forms
- On asymptotics for lacunary partition functions
- Parallel surfaces of the non-lightlike solution of vortex filament equations
- New q-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences
- Kneser-type oscillation theorems for second-order functional differential equations with unbounded neutral coefficients
- Approximation theorems via Pp-statistical convergence on weighted spaces
- Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems
- Theoretical analysis of higher-order system of difference equations with generalized balancing numbers
- On a solvable difference equations system of second order its solutions are related to a generalized Mersenne sequence
- Positive bases, cones, Helly-type theorems
- Digital Jordan surfaces arising from tetrahedral tiling
- Influence of ideals in compactifications
- On the functions ωf and Ωf
- On the 𝓐-generators of the polynomial algebra as a module over the Steenrod algebra, I
- A bivariate distribution with generalized exponential conditionals
- A note on boundary feedback stabilization for degenerate parabolic equations in multi-dimensional domains
