The cyclic groups via the Pascal matrices and the generalized Pascal matrices

Devecı, Ömür; Karaduman, Erdal

doi:10.1016/j.laa.2012.06.024

Cited by 23 publications

(18 citation statements)

References 7 publications

(4 reference statements)

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“…In 20 th century Bridgman [8] , Sedov [9], and Langhaar [10] are sample contributors in this area. Sagiroglu [15], [16], Sagiroglu and Pekşen [17],Ören [18], Khadjiev,Ören and Pekşen [19] and Deveci and Karaduman [20] are some other contributors in this area recently.…”

Section: After Him In 1962 M Nagata Demonstrated the Ring Of G-invarmentioning

confidence: 99%

LS(2)-Equivalence conditions of control points and application to planar Bezier curves

İncesu¹,

Gürsoy²

2017

ntmsci

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Abstract:Having an important role in CAD and CAM systems the Bezier and B-spline curves and surfaces and NURBS modelling are based on control points belongs to these curves and surfaces. So the invariants of these curves and surfaces are the invariants of the control points of these curves and surfaces. In this study we studied the equivalence conditions of compared two different control point systems under the linear similarity transformations LS(2) in R 2 according to the invariant system of these control points. Finally the equivalence conditions of two planar Bezier curves is examined.

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Section: After Him In 1962 M Nagata Demonstrated the Ring Of G-invarmentioning

confidence: 99%

LS(2)-Equivalence conditions of control points and application to planar Bezier curves

İncesu¹,

Gürsoy²

2017

ntmsci

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“…In [5,6,7,17], the authors have produced the cyclic groups and the semigroups via some special matrices and then, they have studied the orders of these algebraic structures. In Section 3, we obtain the cyclic groups and the semigroups by using the generating matrices of the 3-step and 4-step polyhedral sequences of the …rst, second, third, fourth, …fth and sixth kind when read modulo and then, we give their miscellaneous properties.…”

Section: Introductionmentioning

confidence: 99%

The Recurrence Sequences via Polyhedral Groups

Devecı¹,

Aküzüm²

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Abstract. In this paper, we de…ne recurrence sequences by using the relation matrices of the …nite polyhedral groups and then, we obtain some of their properties. Also, we obtain the cyclic groups and the semigroups which are produced by the generating matrices when read modulo and we study the sequences de…ned modulo . Then we derive the relationships between the orders of the cyclic groups obtained and the periods of the sequences de…ned working modulo . Furthermore, we extend these sequences to groups and obtain the periods of the sequences extended in the …nite polyhedral groups case.

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“…Several papers have been recently produced concerning Stirling numbers and cyclic groups, for instance (Broder, 1984) and (Deveci & Akuzum, 2014); or Pascal matrices (Deveci & Karaduman, 2012) and (Hiller, 2016). But they don't seem especially relevant to this article, which essentially deals with basic stuff.…”

Section: Introductionmentioning

confidence: 99%

Arithmetic Triangle

Ferreira¹

2017

JMR

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The product of the first n terms of an arithmetic progression may be developed in a polynomial of n terms. Each one of them presents a coefficient C nk that is independent from the initial term and the common difference of the progression.The most interesting point is that one may construct an "Arithmetic Triangle", displaying these coefficients, in a similar way one does with Pascal's Triangle. Moreover, some remarkable properties, mainly concerning factorials, characterize the Triangle. Other related 'triangles' -eventually treated as matrices -also display curious facts, in their linear modus operandi, such as successive "descendances".

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The cyclic groups via the Pascal matrices and the generalized Pascal matrices

Cited by 23 publications

References 7 publications

LS(2)-Equivalence conditions of control points and application to planar Bezier curves

LS(2)-Equivalence conditions of control points and application to planar Bezier curves

The Recurrence Sequences via Polyhedral Groups

Arithmetic Triangle

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