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Expansion of the Shape of Numbers

DOI: 10.4236/oalib.1107120, PP. 1-18

Subject Areas: Discrete Mathematics

Keywords: Shape of Numbers, Calculation Formula, Combinatorics, Congruence, Stirling Number

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Abstract

This article extends the concept of the shape of numbers. Originally, a shape was defined as [1, K1, K2, ···], 1<K1<K2< ···, KiN. In this paper, the domain of a shape is extended from N to Z, the low bound is extended from 1 to Z, and Ki<Ki 1, Ki=Ki 1, Ki>Ki 1 are allowed, which prove that they can be calculated with the similar form (T0 K0)(T1 K1)(T2 K2) ···. In this way, a lot of calculation formulas can be obtained. At the end, the form is obtained to calculate K1x···xKM (L K1)x···x(L KM) (2L K1)x···x(2L KM) (3L K1)x···x(3L KM) ···.

Cite this paper

Peng, J. (2021). Expansion of the Shape of Numbers. Open Access Library Journal, 8, e7120. doi: http://dx.doi.org/10.4236/oalib.1107120.

References

[1]  Peng, J. (2020) Shape of Numbers and Calculation Formula of Stirling Numbers. Open Access Library Journal, 7, 1-11. https://doi.org/10.4236/oalib.1106081
[2]  Peng, J. (2020) Subdivide the Shape of Numbers and a Theorem of Ring. Open Access Library Journal, 7, 1-14. https://doi.org/10.4236/oalib.1106719
[3]  Peng, J. (2020) Subset of the Shape of Numbers. Open Access Library Journal, 7, 1-15. https://doi.org/10.4236/oalib.1107040

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