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Expansion of the Shape of NumbersDOI: 10.4236/oalib.1107120, PP. 1-18 Subject Areas: Discrete Mathematics Keywords: Shape of Numbers, Calculation Formula, Combinatorics, Congruence, Stirling Number Abstract This article extends the concept of the shape of numbers. Originally, a shape was defined as [1, K1, K2, ···], 1<K1<K2< ···, Ki∈N. 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) ···. 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
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