{'fraction_non_alphanumeric': 0.05649717514124294, 'fraction_numerical': 0.014124293785310734, 'mean_word_length': 4.634920634920635, '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}}
Binary Patterns in Binary Words

We strengthen the description of the 2-avoidable binary patterns given in J. Cassaigne [3], P. Roth [7], and Vanicek [8], by showing that every 2-avoidable binary pattern [t] can be avoided by an infinite independent set of binary words, and, the number of binary words avoiding [t] grows exponentially with their length.