On patterns in sequences of random events
The paper investigates the avoidance of specific patterns in sequences of independent and Markovian trials. Introducing a Markov chain whose states correspond to the possible symbols from the alphabet and to their sequences from the beginning of the word we have to avoid, by using some matrix methods one determines the number of sequences of length \(n\) avoiding the pattern and evaluates the corresponding probabilities. As example one considers the possible configurations of length 3 in the Bernoulli trials.
scientific article; zbMATH DE number 1308338