A characterization of the Bell numbers

被引：50

作者：

Aigner, M ^{[1
]}

机构：

[1] Free Univ Berlin, Inst Math 2, D-14195 Berlin, Germany

来源：

DISCRETE MATHEMATICS | 1999年 / 205卷 / 1-3期

关键词：

D O I：

10.1016/S0012-365X(99)00108-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let B-n be the Bell numbers, and (A) over tilde(n)(n greater than or equal to 0), (B) over tilde(n)(n greater than or equal to 1) be the matrices defined by (A) over tilde(n)(i, j) = Bi+j(0 less than or equal to i, j less than or equal to n), (B) over tilde(n)(i, j) = Bi+j+1(0 less than or equal to i, j less than or equal to n). It is shown that (B-n) is the unique sequence of real numbers such that det (A) over tilde(n) = det (B) over tilde(n) = n!! for all n, where n!! = Pi(k=0)(n)(k!) (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：207 / 210

页数：4