In this study, we define hyperbolic-type k-Fibonacci numbers and then give the relationships between k-step Fibonacci numbers. addition, study sequence modulo m periods of Hperbolic-type sequences for any k which are related m. Furthermore, extend to groups. Finally, obtain 2-Fibonacci in dihedral group D2m, (m ? 2) with respect generating pairs (x,y) (y, x).

Let $$K = {\mathbb {R}}$$ or $${\mathbb {C}}$$ and $${\mathcal {R}}_n$$ be the dihedral quandle of order n. In this article, we give decomposition ring $$K[{\mathcal {R}}_n]$$ into indecomposable right -modules for all even $$n \in {N}}$$ . It follows that given in [2, Prop. 4.18(2)] is valid only case when n not divisible by 4.

Recently, a new parameter of a code, referred to as the remoteness, has been introduced.This parameter can be viewed as a dual to the covering radius. It is exactly determined for the cyclic and dihedral groups. In this paper, we consider the group $U_{6n}$ as a subgroup of $S_{2n+3}$ and obtain its remoteness.  We show that the remoteness of the permutation code $U_{6n}$ is $2n+2$.  Moreover, ...

In the title mol-ecule, C(31)H(26)N(4)O(2)S, the phenyl ring attached to the 1,2,4-triazole ring forms dihedral angles of 65.4 (2), 63.4 (2) and 62.2 (2)° with the other three rings. The 1,2,4-triazole ring makes dihedral angles of 78.0 (2), 87.9 (2), 24.9 (2) and 62.8 (2)° with three phenyl rings and the methoxyphenyl ring.

The cyclic sieving phenomenon of Reiner, Stanton, and White characterizes the stabilizers group actions on finite sets using q-analogue polynomials. Eu Fu demonstrated a generalized cluster complexes every type q-Catalan numbers. In this paper, we exhibit dihedral phenomenon, introduced for odd n by Rao Suk, clusters type. A case, show that Raney numbers count both reflection-symmetric k-angula...