{'fraction_non_alphanumeric': 0.028888888888888888, 'fraction_numerical': 0.005555555555555556, 'mean_word_length': 4.238372093023256, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Algorithms for permutation statistics

Two sequences u; v of n positive integers are order isomorphic if their terms are in the same relative order. A permutation p said to contain permutation q as a pattern if there is some subsequence of p which is order isomorphic to q. This subsequence is called a copy of q. This notion of pattern containment is generalized to include adjacency restrictions as per dashed patterns. The primary permutation statistics studied in this work are written in terms of the number of copies of a given pattern or patterns. The central concern of this thesis is to compute answers to problems of the following type: Given patterns q_1, q_2, ..., q_t and nonnegative numbers k_1, k_2, ..., k_t how many permutations in Sn have k_i copies of q_i for each i?" The techniques which apply will depend on the nature of the patterns (i), as well as whether or not all k_i = 0.