Geodesic
Parafunctions of triangular matrices and~$m$-ary~partitions of numbers
Algebra and discrete mathematics, Tome 21 (2016) no. 1, pp. 144-152.

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Using the machinery of paradeterminants and parapermanents developed in [2] we get new relations for some number-theoretical functions natural argument that were studied in [3].
Keywords: $m$-ary partition.
Mots-clés : partition polynomials, triangular matrices, paradeterminant, parapermanent 
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Svitlana Steflyuk; Roman Zatorsky. Parafunctions of triangular matrices and~$m$-ary~partitions of numbers. Algebra and discrete mathematics, Tome 21 (2016) no. 1, pp. 144-152. http://geodesic.mathdoc.fr/item/ADM_2016_21_1_a9/

[1] Zatorsky R. A., “Theory of paradeterminants and its applications”, Algebra and Discrete Mathematics, 2007, no. 1, 109–138 | MR | Zbl

[2] Zatorsky R. A., Calculus of Triangular Matrices and Its Applications, Simyk, Ivano-Frankivsk, 2010, 508 pp. (Ukrainian)

[3] Yasuyuki Kachi and Pavlos Tzermias, “On the $m$-ary partition numbers”, Algebra and Discrete Mathematics, 19:1 (2015), 67–76 | MR | Zbl

[4] J.-P. Allouche, J. Shallit, “The ubiquitous Prouhet-Thue-Morse sequence”, Sequences and their Aplications, Proceedings of SETA '98, eds. C. Ding et al., Springer-Verlag, London, 1999, 1–16 | DOI | MR | Zbl

[5] R. A. Zatorsky, “Researching of Hessenbergs matrix functions”, Carpathian Mathematical Publications, 3:1 (2011), 49–55 (Ukrainian) | MR | Zbl

[6] Riordan J., Combinatorial identities, Wiley, New York, 1968, 256 pp. | MR | Zbl

[7] R. Zatorsky, S. Stefluk, “On one class of partition polynomials”, Algebra and Discrete Mathematics, 16:1 (2013), 127–133 | MR | Zbl