TOPICS

# Interspersion

An array , of positive integers is called an interspersion if

1. The rows of comprise a partition of the positive integers,

2. Every row of is an increasing sequence,

3. Every column of is a (possibly finite) increasing sequence,

4. If and are distinct rows of and if and are any indices for which , then .

If an array is an interspersion, then it is a sequence dispersion. If an array is an interspersion, then the sequence given by for some is a fractal sequence. Examples of interspersion are the Stolarsky array and Wythoff array.

Fractal Sequence, Sequence Dispersion, Stolarsky Array

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## References

Kimberling, C. "Interspersions and Dispersions." Proc. Amer. Math. Soc. 117, 313-321, 1993.Kimberling, C. "The First Column of an Interspersion." Fib. Quart. 32, 301-314, 1994.Kimberling, C. "Fractal Sequences and Interspersions." Ars Combin. 45, 157-168, 1997.Kimberling, C. "Interspersions and Dispersions." http://faculty.evansville.edu/ck6/integer/intersp.html.

Interspersion

## Cite this as:

Weisstein, Eric W. "Interspersion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Interspersion.html