“Fractal Sequence”的概念、定义、习题解题方法及翻译-数学辞典

单词

Fractal Sequence

释义

Fractal Sequence

Given an Infinitive Sequence with associated array , then is said to be a fractal sequence

: 1. If , then there exists such that ,
: 2. If , then, for every , there is exactly one such that .

(As

and

range through

, the array

, called the associative array of

, ranges through all of

.)An example of a fractal sequence is 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 1, 3, 2, 1, 3, ....

If is a fractal sequence, then the associated array is an Interspersion. If is a fractal sequence, thenthe Upper-Trimmed Subsequence is given by , and the Lower-Trimmed Subsequence is anotherfractal sequence. The Signature of an Irrational Number is a fractal sequence.

See also Infinitive Sequence

References

Kimberling, C. ``Fractal Sequences and Interspersions.'' Ars Combin. 45, 157-168, 1997.

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