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Counting cycles and finite dimensional Lp norms

Igor Rivin
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Abstract

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.

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Igor Rivin. 2001-11-09. Counting cycles and finite dimensional Lp norms. https://arxiv.org/abs/math/0111106

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