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An approach to the moments subset sum problem through systems of diagonal equations over finite fields
Let be the finite field of elements, for a given subset
, , an integer and
we are interested in determining the
existence of a subset of cardinality such that for . This problem is known as the moment subset sum
problem and it is -complete for a general . We make a novel approach of
this problem trough algebraic geometry tools analyzing the underlying variety
and employing combinatorial techniques to estimate the number of
-rational points on certain varieties. We managed to give
estimates on the number of -rational points on certain diagonal
equations and use this results to give estimations and existence results for
the subset sum problem.Comment: 25 page