|
Open Access Library Journal 1 2021
Expansion of the Shape of NumbersDOI: 10.4236/oalib.1107120, PP. 1-18 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) ···.
|