Dispersion (Sequence)

An array $B=b_{ij}$, $i,j\geq 1$ of Positive Integers is called a dispersion if

1. The first column of $B$ is a strictly increasing sequence, and there exists a strictly increasing sequence $\{s_k\}$ such that

2. $b_{12}=s_1\geq 2$,

3. The complement of the Set $\{b_{i1}: i\geq 1\}$ is the Set $\{s_k\}$,

4. $b_{ij}=s_{b_{i,j-1}}$ for all $j\geq 3$ for $i=1$ and for all $g\geq 2$ for all $i\geq 2$.

If an array $B=b_{ij}$ is a dispersion, then it is an Interspersion.

See also Interspersion

References

Kimberling, C. ``Interspersions and Dispersions.'' Proc. Amer. Math. Soc. 117, 313-321, 1993.