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math.NT2015
On sets free of sumsets with summands of prescribed size
Javier Cilleruelo, Rafael Tesoro
We study extremal problems about sets of integers that do not contain sumsets with summands of prescribed size. We analyse both finite sets and infinite sequences. We also study th…
math.NT2013
Sets of integers avoiding congruent subsets
Rafael Tesoro
Consider the sets of integers that avoid any arrangement of congruent -subsets. Our findings refine and improve upon some results by Erdős and Harzheim about these sets.
math.NT2012
Dense infinite sequences
Javier Cilleruelo, Rafael Tesoro
For and we prove the existence of infinite sequences $\B$ with counting function This result extends a cons…