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Balances in the Set of Arithmetic Progressions
Axioms, 2021 This article focuses on searching and classifying balancing numbers in a set of arithmetic progressions. The sufficient and necessary conditions for the existence of balancing numbers are presented.
Chan-Liang Chung +2 more
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The Balancing Number and Generalized Balancing Number of Some Graph Classes
The Electronic Journal of Combinatorics, 2023 Given a graph $G$, a 2-coloring of the edges of $K_n$ is said to contain a balanced copy of $G$ if we can find a copy of $G$ such that half of its edges is in each color class. If there exists an integer $k$ such that, for $n$ sufficiently large, every 2-coloring of $K_n$ with more than $k$ edges in each color contains a balanced copy of $G$, then we ...
Dailly, Antoine +3 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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Two generalizations of dual-complex Lucas-balancing numbers
Acta Universitatis Sapientiae: Mathematica, 2022 In this paper, we study two generalizations of dual-complex Lucas-balancing numbers: dual-complex k-Lucas balancing numbers and dual-complex k-Lucas-balancing numbers.
D. Bród, A. Szynal-Liana, I. Włoch
semanticscholar +1 more source
A Study on Generalized Balancing Numbers
Asian Journal of Advanced Research and Reports, 2021 In this paper, we investigate properties of the generalized balancing sequence and we deal with, in detail, namely, balancing, modified Lucas-balancing and Lucas-balancing sequences.
Y. Soykan
semanticscholar +1 more source
A probabilistic approach to the geometry of the ℓᵨⁿ-ball [PDF]
, 2016 This article investigates, by probabilistic methods, various geometric questions on Bᵨⁿ, the unit ball of ℓᵨⁿ. We propose realizations in terms of independent random variables of several distributions on Bᵨⁿ, including the normalized volume measure ...
Barthe, Franck +3 more
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On tridimensional Lucas-balancing numbers and some properties [PDF]
Notes on Number Theory and Discrete MathematicsIn this article, we introduce the tridimensional version of the Lucas-balancing numbers based on the unidimensional version, and we also study some of their properties and sum identities.
J. Chimpanzo +2 more
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How to sum powers of balancing numbers efficiently [PDF]
Notes on Number Theory and Discrete Mathematics, 2020 Balancing numbers possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of balancing numbers can be summed explicitly. For this, as a first step, a power B_n^l is expressed as a linear combination of B_{mn}.
H. Prodinger
semanticscholar +1 more source
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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BALANCING, PELL AND SQUARE TRIANGULAR FUNCTIONS [PDF]
, 2015 In this work, we derive some functions on balancing, cobalancing, Lucas-balancing, Lucas-cobalancing, Pell, Pell-Lucas and square triangular numbers. At the end of this article we investigated common values of combinatorial numbers and Lucas-balancing ...
Olajos, Péter +2 more
core +2 more sources