{'fraction_non_alphanumeric': 0.015544041450777202, 'fraction_numerical': 0.0, 'mean_word_length': 4.979381443298969, '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}}
On Subsets of Ordered Trees Enumerated by a Subsequence of Fibonacci Numbers

In this paper, we provide a bijection between subsets of ordered trees with n edges where no two vertices at the same level have di↵erent parents and those with height at most three. We show that the number of these subsets of ordered trees corresponds to every other Fibonacci number, and provide a combinatorial interpretation of Chen and Shapiro’s generalization of this sequence using k-trees. We also prove Shapiro’s identity involving the generating function of this sequence and Riordan arrays.