“Nonnegative Partial Sum”的概念、定义、习题解题方法及翻译-数学辞典

单词

Nonnegative Partial Sum

释义

Nonnegative Partial Sum

The number of sequences with Nonnegative partial sums which can be formed from 1s and s (Bailey 1996,Brualdi 1992) is given by the Catalan Numbers. Bailey (1996) gives the number of Nonnegativepartial sums of 1s and s , , ..., , so that

(1)

for all

. The closed form expression is

(2)

for

(3)

for

, and

(4)

for

. Setting

then recovers the Catalan Numbers

(5)

See also Catalan Number

References

Bailey, D. F. ``Counting Arrangements of 1's and 's.'' Math. Mag. 69, 128-131, 1996.

Brualdi, R. A. Introductory Combinatorics, 2nd ed. New York: Elsevier, 1992.

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