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A sequence number is a consecutive number in a sequence of numbers, usually of real integers (natural numbers).Sequence numbers have many practical applications. They can be used, among other things, as part of serial numbers on manufactured parts, in case management, [1] or in databases as a surrogate key for registering and identifying unique entries in a table [2] [3] (in which case it is ...
The nth element of a Fibonacci word, , is 1 if the Zeckendorf representation (the sum of a specific set of Fibonacci numbers) of n includes a 1, and 0 if it does not include a 1. The digits of the Fibonacci word may be obtained by taking the sequence of fibbinary numbers modulo 2. [10]
The easiest way to make a recurrent sequence is to form a periodic sequence, one where the sequence repeats entirely after a given number m of steps. Such a sequence is then uniformly recurrent and n X can be set to any multiple of m that is larger than twice the length of X. A recurrent sequence that is ultimately periodic is purely periodic. [2]
If s is an infinite sequence word and w is a finite word, let μ N (w) denote the number of occurrences of w as a factor in the prefix of s of length N + |w| − 1. If μ N (w) has a limit as N→∞, we call this the frequency of w, denoted by μ(w). [4]: 73 For a Sturmian word s, every finite factor has a frequency.
Over a ternary alphabet, a square-free word of length more than 13 contains all the square-free two-letter combinations. [12] This can be proved by constructing a square-free word without the two-letter combination ab. As a result, bcba cbca cbaca is the longest square-free word without the combination ab and its length is equal to 13.
The number itself, which may appear in various places on the page, can be referred to as a page number or as a folio. [1] Like other numbering schemes such as chapter numbering, page numbers allow the citation of a particular page of the numbered document and facilitates to the reader to find specific parts of the document and to know the size ...
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A free group has a unique normal form i.e. each element in is represented by a unique reduced word. Proof. An elementary transformation of a word w ∈ G {\displaystyle w\in G} consists of inserting or deleting a part of the form a a − 1 {\displaystyle aa^{-1}} with a ∈ S ± {\displaystyle a\in S^{\pm }} .