# Sharp bounds for sums associated to graphs of matrices

@article{Mingo2012SharpBF, title={Sharp bounds for sums associated to graphs of matrices}, author={J. Mingo and R. Speicher}, journal={Journal of Functional Analysis}, year={2012}, volume={262}, pages={2272-2288} }

We provide a simple algorithm for finding the optimal upper bound for sums of products of matrix entries of the form
Sπ(N):=∑j1,…,j2m=1kerj⩾πNtj1j2(1)tj3j4(2)⋯tj2m−1j2m(m)
where some of the summation indices are constrained to be equal. The upper bound is easily obtained from a graph Gπ associated to the constraints, π, in the sum.

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