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- W4381551244 abstract "Dyck paths (also balanced brackets and Dyck words) are among the most heavily studied Catalan families. This paper is a continuation of [2, 3, 4]. In the paper we are dealing with the numbering of Dyck paths, with the resulting numbers, the terms of the OEIS sequence A036991, which encode Dyck paths and which we have called the Dyck numbers. In this sequence, it turned out to be promising to investigate nested term patterns. The sequence is constructed entirely from nested patterns, with each pattern having an infinite number of copies. We have already considered repeated triplets of adjacent odd numbers; copies of such triplets in the process of expansion form quite complex structures, the analysis of which allows us to understand the structure of A036991. Additionally, we note that the composition of the terms of each pattern is repeated many times by a simple shift (offset) of Dyck numbers by some fixed value. As a result, pattern copies give us important parts of most levels and even give us new levels." @default.
- W4381551244 created "2023-06-22" @default.
- W4381551244 creator A5034134617 @default.
- W4381551244 date "2023-06-17" @default.
- W4381551244 modified "2023-10-18" @default.
- W4381551244 title "Dyck Numbers, IV. Nested patterns in OEIS A036991" @default.
- W4381551244 doi "https://doi.org/10.48550/arxiv.2306.10318" @default.
- W4381551244 hasPublicationYear "2023" @default.
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