The visibility parameter for words and permutations
We investigate the visibility parameter, i.e., the number of visible pairs, first for words over a finite alphabet, then for permutations of the finite set {1, 2, …, n}, and finally for words over an infinite alphabet whose letters occur with geometric probabilities. The results obtained for permutations correct the formula for the expectation obtained in a recent paper by Gutin et al. [Gutin G., Mansour T., Severini S., A characterization of horizontal visibility graphs and combinatorics on words,...