A bijection between atomic partitions and unsplitable partitions.
Chen, William Y.C., Li, Teresa X.S., Wang, David G.L. (2011)
The Electronic Journal of Combinatorics [electronic only]
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Chen, William Y.C., Li, Teresa X.S., Wang, David G.L. (2011)
The Electronic Journal of Combinatorics [electronic only]
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Vella, David C. (2008)
Integers
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Zhao, Haijian, Zhong, Zheyuan (2011)
The Electronic Journal of Combinatorics [electronic only]
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Andrews, George E. (2004)
The Electronic Journal of Combinatorics [electronic only]
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Bagno, Eli, Butman, Ayelet, Garber, David (2007)
The Electronic Journal of Combinatorics [electronic only]
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Killpatrick, Kendra (2005)
The Electronic Journal of Combinatorics [electronic only]
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Faliharimalala, Hilarion L.M., Zeng, Jiang (2008)
The Electronic Journal of Combinatorics [electronic only]
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Grainger, Arthur D. (2003)
International Journal of Mathematics and Mathematical Sciences
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Guersenzvaig, Natalio H., Spivey, Michael Z. (2007)
Integers
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Grosjean, Carl C. (1996)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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De Coster, C., Habets, P. (1996)
Portugaliae Mathematica
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T. Karthick, C.R. Subramanian (2013)
Discussiones Mathematicae Graph Theory
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A star coloring of an undirected graph G is a coloring of the vertices of G such that (i) no two adjacent vertices receive the same color, and (ii) no path on 4 vertices is bi-colored. The star chromatic number of G, χs(G), is the minimum number of colors needed to star color G. In this paper, we show that if a graph G is either non-regular subcubic or cubic with girth at least 6, then χs(G) ≤ 6, and the bound can be realized in linear time.
Wancang Ma, David Minda (1993)
Annales Polonici Mathematici
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Recently, A. W. Goodman introduced the class UCV of normalized uniformly convex functions. We present some sharp coefficient bounds for functions f(z) = z + a₂z² + a₃z³ + ... ∈ UCV and their inverses . The series expansion for converges when , where depends on f. The sharp bounds on and all extremal functions were known for n = 2 and 3; the extremal functions consist of a certain function k ∈ UCV and its rotations. We obtain the sharp bounds on and all extremal functions for...