Counting occurrences of a pattern in a binary word

Enumerating the number of times one word occurs in another is a much-studied combinatorial subject. By utilizing a method that we call ``lexicographic extreme referencing'', we provide a formula for computing occurrences of one binary word in another. We then study Bn,p(k), the number of binary words of length n containing a given word p exactly k times. For this purpose, we first use lexicographic extreme referencing to provide an algorithm for constructing all words w that contain a given word p. Afterward, we give a modified version of this algorithm for constructing the subset of binary words that are ``primitive'' with respect to p, and we discuss approaches for finding Bn,p(k) via primitive words.