TITLE:
Shape of Numbers and Calculation Formula of Stirling Numbers
AUTHORS:
Ji Peng
KEYWORDS:
Combinatorics, Shape of Numbers, Stirling Numbers, Congruence Formula
JOURNAL NAME:
Open Access Library Journal,
Vol.7 No.3,
March
23,
2020
ABSTRACT: This article investigated the idea of Shape of numbers and introduced new operators. The idea divides all products of k distinct integers in [1, n - 1] into 2K-1 catalogs and derives the calculation formula of every catalog. As a simple deduction, a direct formula of the Stirling numbers of the first kind S1(n, n - k) and a simple recursive formula of Stirling numbers of the second kind S2(n, n - k) are obtained. By analyzing the Shape of numbers, new congruence formulas are obtained.