Some groups of Fibonacci type
نویسندگان
چکیده
منابع مشابه
Groups of Fibonacci Type Revisited
This article concerns a class of groups of Fibonacci type introduced by Johnson and Mawdesley that includes Conway’s Fibonacci groups, the Sieradski groups, and the Gilbert-Howie groups. This class of groups provides an interesting focus for developing the theory of cyclically presented groups and, following questions by Bardakov and Vesnin and by Cavicchioli, Hegenbarth, and Repovš, they have ...
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We introduce polynomial generalizations of the r-Fibonacci, r-Gibonacci, and rLucas sequences which arise in connection with two statistics defined, respectively, on linear, phased, and circular r-mino arrangements.
متن کاملSome Properties of Fibonacci Numbers
We formalized some basic properties of the Fibonacci numbers using definitions and lemmas from [7] and [23], e.g. Cassini’s and Catalan’s identities. We also showed the connections between Fibonacci numbers and Pythagorean triples as defined in [31]. The main result of this article is a proof of Carmichael’s Theorem on prime divisors of prime-generated Fibonacci numbers. According to it, if we ...
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where the subscripts are reduced modulo n, and r ≥ 2, n ≥ 2. We also denote in short the above presentation by F (r, n, s, p) = Gn(x1x1+p · · ·x1+p(r−1)x 1+s) according to notation in [13] and [16]. This family contains many classes of cyclic presentations of groups, previously considered by several authors. The groups F (2, n, 2, 1) are the Fibonacci groups F (2, n) = Gn(x1x2x 3 ) introduced b...
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We observe that, for fixed n ≥ 3, each of the Artin groups of finite type An, Bn = Cn, and affine type Ãn−1 and C̃n−1 is a central extension of a finite index subgroup of the mapping class group of the (n + 2)-punctured sphere. (The centre is trivial in the affine case and infinite cyclic in the finite type cases). Using results of Ivanov and Korkmaz on abstract commensurators of surface mapping...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1975
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700020498