Counting cycles and finite dimensional Lp norms
Combinatorics
2007-05-23 v1 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.math/0111106,
title = {Counting cycles and finite dimensional Lp norms},
author = {Igor Rivin},
journal= {arXiv preprint arXiv:math/0111106},
year = {2007}
}
Comments
considerable extension of math.CO/9910093