Sharp Bounds for Sums Associated to Graphs of Matrices
Operator Algebras
2012-10-25 v1 Combinatorics
Abstract
We provide a simple algorithm for finding the optimal upper bound for sums of products of matrix entries of the form S_pi(N) := sum_{j_1, ..., j_2m = 1}^N t^1_{j_1 j_2} t^2_{j_3 j_4} ... t^m_{j_2m-1 j_2m} where some of the summation indices are constrained to be equal. The upper bound is easily obtained from a graph G associated to the constraints in the sum.
Keywords
Cite
@article{arxiv.0909.4277,
title = {Sharp Bounds for Sums Associated to Graphs of Matrices},
author = {James A. Mingo and Roland Speicher},
journal= {arXiv preprint arXiv:0909.4277},
year = {2012}
}
Comments
20 pages