Sharp Bounds for Sums Associated to Graphs of Matrices
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_2m1 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2009
 arXiv:
 arXiv:0909.4277
 Bibcode:
 2009arXiv0909.4277M
 Keywords:

 Mathematics  Operator Algebras;
 Mathematics  Combinatorics;
 05C90;
 62E20
 EPrint:
 20 pages