Abstract
In this paper, we propose the modelling of patterns of financial transactions - with a focus on the domain of cryptocurrencies - as splittings and present a method for generating such splittings utilizing integer partitions. We further exemplify that, by having these partitions fulfill certain criteria derived from financial policies, the splittings generated from them can be used for modelling illicit transactional behavior as seen in smurfing.
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Notes
- 1.
- 2.
We assume the existence of a smallest currency unit; in the real world, this assumption holds—in particular—for the US$, for the Euro and for Bitcoin.
- 3.
Each element p of S(n) is a finite sequence, we write \(p=(p(1),p(2),\dots ,p(\text {length}(p))\).
- 4.
- 5.
Here, we adopt the notation from SageMath and denote sequences as \([\lambda _1, \dots , \lambda _r]\).
- 6.
Note that it follows from Definition 1 that we have \(\lambda _{i+1}-\lambda _{i}\le 0\), for all \(1 \le i<r\).
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Acknowledgements
SBA Research (SBA-K1) is a COMET Center within the COMET - Competence Centers for Excellent Technologies Programme and funded by BMK, BMAW, and the federal state of Vienna. The COMET Programme is managed by FFG. Moreover, this work was performed partly under the following financial assistance award 70NANB21H124 from U.S. Department of Commerce, National Institute of Standards and Technology.
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Garn, B., Kieseberg, K., Çulha, C., Koelbing, M., Simos, D.E. (2023). A Mathematical Approach on the Use of Integer Partitions for Smurfing in Cryptocurrencies. In: Pardalos, P., Kotsireas, I., Knottenbelt, W.J., Leonardos, S. (eds) Mathematical Research for Blockchain Economy. MARBLE 2023. Lecture Notes in Operations Research. Springer, Cham. https://doi.org/10.1007/978-3-031-48731-6_10
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