New results on Nyldon words and Nyldon-like sets

Grinberg defined Nyldon words as those which cannot be factorized into a sequence of lexicographically nondecreasing smaller words. He was inspired by Lyndon words, the same way except with "nondecreasing" replaced "nonincreasing." Charlier, Philibert, and Stipulanti proved that, like any word has unique factorization They also show that form right Lazard set, equivalently, Hall set. In this paper, we provide new proof related to set theory resolve several questions Charlier et al. particular, prove fixed length circular code, result on factorizing powers investigate procedure for generating We these results generalize class sets, are an example, name "Nyldon-like sets."