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Expansion of the Shape of Numbers

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

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) ···.

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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