## Neural Computation

With the development of multielectrode recording techniques, it is possible to measure the cell firing patterns of multiple neurons simultaneously, generating a large quantity of data. Identification of the firing patterns within these large groups of cells is an important and a challenging problem in data analysis. Here, we consider the problem of measuring the significance of a repeat in the cell firing sequence across arbitrary numbers of cells. In particular, we consider the question, given a ranked order of cells numbered 1 to *N*, what is the probability that another sequence of length *n* contains *j* consecutive increasing elements? Assuming each element of the sequence is drawn with replacement from the numbers 1 through *N*, we derive a recursive formula for the probability of the sequence of length *j* or more. For *n* < 2*j*, a closed-form solution is derived. For *n* ≥ 2*j*, we obtain upper and lower bounds for these probabilities for various combinations of parameter values. These can be computed very quickly. For a typical case with small *N* (<10) and large *n* (<3000), sequences of 7 and 8 are statistically very unlikely. A potential application of this technique is in the detection of repeats in hippocampal place cell order during sleep. Unlike most previous articles on increasing runs in random lists, we use a probability approach based on sets of overlapping sequences.