Counting cycles and finite dimensional Lp norms

Details Counting cycles and finite dimensional Lp norms Counting cycles and finite dimensional Lp norms

2001-11-09

arxiv.org/abs/math/0111106v1

Mathematics

Combinatorics

considerable extension of math.CO/9910093

Scientific paper

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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