An array A=a_(ij), i,j>=1 of positive integers is called an interspersion if

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

2. Every row of A is an increasing sequence,

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

4. If (u_j) and (v_j) are distinct rows of A and if p and q are any indices for which u_p<v_q<u_(p+1), then u_(p+1)<v_(q+1)<u_(p+2).

If an array A=a_(ij) is an interspersion, then it is a sequence dispersion. If an array A=a(i,j) is an interspersion, then the sequence {x_n} given by {x_n=i:n=(i,j)} for some j is a fractal sequence. Examples of interspersion are the Stolarsky array and Wythoff array.

See also

Fractal Sequence, Sequence Dispersion, Stolarsky Array

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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."

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Cite this as:

Weisstein, Eric W. "Interspersion." From MathWorld--A Wolfram Web Resource.

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