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To mitigate the conflict of economic development and ecological protection, China government initiates its national park plan in recent years. In this stage, addressing the benefit contradictories among stakeholders is of importance. Around this issue, this paper focuses on the one of most keen-edged topics in China, which is how to deal well with the coordination issue among local government, tourism development enterprise and local residents. To disentangle the complexly dynamic relationships among them, a set of mathematical models are built and derived, based on evolutionary game theory. The corresponding results indicate that the intensity of regulation by local governments, the degree of compensation to ecotourism development projects by tourism development enterprises, and the participation degree of local residents to the projects are closely related to ultimate game stabilization; some propositions are gained accordingly, which suggest the bounded conditions to achieve the optimal stabilization. To validate and broaden the results, the relevant numerical simulation and discussion are provided. • The stakeholders relationship about China's National Park Ecotourism is discussed. • The corresponding evolutionary game models are built and analyzed. • The optimal conditions of advancing the ecotourism of national parks are put forth. [ABSTRACT FROM AUTHOR]

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