Results 231 to 240 of about 85,264 (264)
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On the number of balanced signed graphs
The Bulletin of Mathematical Biophysics, 1967The classical enumeration theorem of Polya (Acta Math.,68, 145–254, 1937) is applied to a modified version of Harary’s (Pacific J. Math.,8, 743–755, 1958) generating functions for counting bicolored graphs to derive a counting function for the number of balanced signed graphs. Methods for computing these counting polynomial functions are discussed.
Harary, Frank, Palmer, Edgar M.
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Factoriangular numbers in balancing and Lucas-balancing sequence
Boletín de la Sociedad Matemática Mexicana, 2020The balancing numbers \(\{B_n\}_{n\ge 0}\) have initial terms \(B_0=0,~B_1=1\) and satisfy the recurrence \(B_{n+2}=6B_{n+1}-B_n\) for all \(n\ge 0\). The Lucas-balancing numbers \(\{C_n\}_{n\ge 0}\) have initial terms \(C_0=1,~C_1=3\) and satisfy the same recurrence relation as the balancing numbers.
Sai Gopal Rayaguru +2 more
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The maximum number of balancing sets
Graphs and Combinatorics, 1987Let \(a_ 1,...,a_ n\) be a sequence of nonzero real numbers such that \(\sum^{n}_{i=1}a_ i=0\). B is called a balancing set if \(\sum_{b\in B}a_ b=0\). Let f(n) be the maximum number of balancing sets. It is shown that \(f(n)=\left( \begin{matrix} 2k\\ k\end{matrix} \right)\) if \(n=2k\) and \(f(n)=2\left( \begin{matrix} 2k\\ k-1\end{matrix} \right ...
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On the Periodicity of Lucas-Balancing Numbers and p-adic Order of Balancing Numbers
Iranian Journal of Science and Technology, Transactions A: Science, 2020The objective of this article is to study the periodicity of Lucas-balancing numbers modulo any positive integer. Some relations between the periodicity of balancing and Lucas-balancing numbers are also discussed. Further, in this study the p-adic order of balancing numbers is completely characterized .
Takao Komatsu +2 more
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INCOMPLETE BALANCING AND LUCAS-BALANCING NUMBERS
2018The aim of this article is to establish some combinatorial expressions of balancing and Lucas-balancing numbers and investigate some of their properties.
Patel, Bijan Kumar +2 more
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Ars Combinatoria
Behera and Panda defined a balancing number as a number b for which the sum of the numbers from 1 to b – 1 is equal to the sum of the numbers from b + 1 to b + r for some r. They also classified all such numbers. We define two notions of balancing numbers for Farey fractions and enumerate all possible solutions.
Noah Lebowitz-Lockard, Joseph Vandehey
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Behera and Panda defined a balancing number as a number b for which the sum of the numbers from 1 to b – 1 is equal to the sum of the numbers from b + 1 to b + r for some r. They also classified all such numbers. We define two notions of balancing numbers for Farey fractions and enumerate all possible solutions.
Noah Lebowitz-Lockard, Joseph Vandehey
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The Balanced Decomposition Number and Vertex Connectivity
SIAM Journal on Discrete Mathematics, 2010Summary: The balanced decomposition number \(f(G)\) of a graph \(G\) was introduced by \textit{S. Fujita} and \textit{T. Nakamigawa} [Discrete Appl. Math. 156, No. 18, 3339--3344 (2008; Zbl 1178.05075)]. A balanced coloring of a graph \(G\) is a coloring of some of the vertices of \(G\) with two colors, such that there is the same number of vertices in
Shinya Fujita 0001, Henry Liu
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The number oft-wise balanced designs
Combinatorica, 1991This paper provides asymptotically the number of \(t\)-wise balanced designs and the number of \(t\)-profiles. If these numbers are indicated by \(N_ t(n)\) and \(P_ t(n)\), respectively, then the authors show that \[ N_ t(n)=n^{[{n\choose t}/(t+1)](1+o(1))} \] and \[ \exp(c_ 1\sqrt n\log n)\leq P_ t(n)\leq\exp(c_ 2\sqrt n\log n) \] where \(o(1)\) is ...
Charles J. Colbourn +4 more
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New Hybrid Numbers with Balancing and Lucas-Balancing Number Components
2023Nurkan, Semra +3 more
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A model based balancing system for battery energy storage systems
Journal of Energy Storage, 2022Xuesong Mei, Jun Xu, Zheng Sun
exaly