Results 21 to 30 of about 1,621,283 (291)
On the Number of Balanced Lines [PDF]
Discrete & Computational Geometry, 2001 Given a set of \(n\) black and \(n\) white points in general position in the plane, a line \(l\) determined by two of them is said to be balanced, if each open halfplane determined by \(l\) contains exactly the same number of white points and black points. The authors prove that the number of balanced lines is at least \(n\).
Pach, János, Pinchasi, Rom
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On the Properties of Balancing and Lucas-Balancing $p$-Numbers
Iranian Journal of Mathematical Sciences and Informatics, 2022 Summary: The main goal of this paper is to develop a new generalization of balancing and Lucas-balancing sequences namely balancing and Lucas-balancing \(p\)-numbers and derive several identities related to them. Some combinatorial forms of these numbers are also presented.
Behera, Adikanda, Ray, Prasanta Kumar
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The Number of Generalized Balanced Lines [PDF]
Discrete & Computational Geometry, 2010 6 pages, 3 figures, several typos fixed, reference ...
David Orden +2 more
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The Journal of the Indian Mathematical Society, 2020 For each positive integer k, the Diophantine equation (k+1)+(k+2)+···+(n−1) = (n+1)+(n+2)+···+(n+r) is studied.
Rayaguru, S. G. +2 more
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SOME ALGEBRAIC RELATIONS ON BALANCING NUMBERS [PDF]
, 2017 WOS: 000401308200018In this work we deduce some new algebraic relations on balancing numbers and their relationships with Pell, Pell-Lucas and oblong numbers.
Tekcan, Ahmet +2 more
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On the Balanced Decomposition Number [PDF]
Graphs and Combinatorics, 2015 A {\em balanced coloring} of a graph $G$ means a triple $\{P_1,P_2,X\}$ of mutually disjoint subsets of the vertex-set $V(G)$ such that $V(G)=P_1 \uplus P_2 \uplus X$ and $|P_1|=|P_2|$. A {\em balanced decomposition} associated with the balanced coloring $V(G)=P_1 \uplus P_2 \uplus X$ of $G$ is defined as a partition of $V(G)=V_1 \uplus \cdots \uplus ...
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Fascinating Number Sequences from Fourth Order Difference Equation Via Quaternion Algebras
Discussiones Mathematicae - General Algebra and Applications, 2021 The balancing and Lucas-balancing numbers are solutions of second order recurrence relations. A linear combination of these numbers can also be obtained as solutions of a fourth order recurrence relation.
Patra Asim
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The Solution of a System of Higher-Order Difference Equations in Terms of Balancing Numbers
Pan-American Journal of Mathematics, 2023 In this paper, we are interested in the closed-form solution of the following system of nonlinear difference equations of higher order, un+1 = 1/34-vn-m , vn+1 = 1/34-un-m, n, m ∈ N0, and the initial values u-j and v-j , j∈{0, 1, ..., m} are real numbers
Ahmed Ghezal, Imane Zemmouri
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A study on the number of edges of some families of graphs and generalized Mersenne numbers
Ratio Mathematica, 2022 The relationship between the Nandu sequence of the SM family of graphs and the Generalized Mersenne numbers is demonstrated in this study. Nandu sequences are related to the two families of SM sum graphs and SM Balancing graphs.
K.G. Sreekumar +3 more
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Journal of Innovative Applied Mathematics and Computational Sciences, 2021 In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ for generalized balancing numbers are presented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.
Yüksel Soykan +2 more
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