Abstract: We often observe the occurrence or non-occurrence of a special kind of event over time or space. For instance we want to know if each year was a record year or if each point represented a flaw or not, or if catch represented a new species or not, or if each co-ordinate in a random permutation was the end of a "cycle" or not, and so on. Such a sequence can be represented by Bernoulli random variables $(Y_1, Y_2, \cdots)$ with each $Y_n$ taking values $0$ or $1$.

One is interested in the frequency (or counts) $(Z_1, Z_2, Z_3, \cdots)$ of special patterns (or strings) of the form $\{11\}, \{101\}, \{1001\}, \cdots$ in the Bernoulli sequence.

This problem has been treated by combinatorial methods in the literature which are unintuitive and cumbersome. We will give a sample of such a combinatorial method. In this talk, we will show how we can embed this problem in Poisson process with marks and obtain the distributions of counts of strings in a general way.