Sequence Dispersion

An array ,  of positive integers is called a dispersion if

1. The first column of  is a strictly increasing sequence, and there exists a strictly increasing sequence  such that

2. ,

3. The complement of the set  is the set ,

4.  for all  for  and for all  for all .

If an array  is a dispersion, then it is an interspersion.

REFERENCES:

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