Counting cycles and finite dimensional Lp norms

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We obtain sharp bounds for the number of n--cycles in a finite graph as a function of the number of edges, and prove that the complete graph is optimal in more ways than could be imagined. We prove sharp estimates on both the sum of k-th powers of the coordinates and the Lk norm subject to the constraints that the sum of squares of the coordinates is fixed, and that the sum of the coordinates vanishes.
considerable extension of math.CO/9910093

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Combinatorics, Classical Analysis and ODEs, 05C38, 49N99

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http://salesiana.dossiersoluciones.com/handle/123456789/62606

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0111106
 http://arxiv.org/abs/math/0111106

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arXiv