Mario Huicochea

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Given a universe (a set) U and a property P, (closed under inclusions, for subsets of U). Results of the type “if every subset of cardinality μ of a finite family F ⊂ U has property P, then the entire family F has property P”are called Helly type theorems. The minimum number μ for which the result is true is called the Helly number of the Helly-type theorem(More)
In this paper, we extend the definition of the Nathanson height from points in projective spaces over Fp to points in projective spaces over arbitrary finite fields. If [a0 : . . . : an] ∈ P(Fp), then the Nathanson height is hp([a0 : a1 : . . . : ad]) = min b∈Fp d ∑ i=0 H(bai) where H(ai) = |N(ai)|+p(deg(ai)−1) with N the field norm and |N(ai)| the element(More)
Let p be a prime number and Zp be the cyclic group of order p. A coloring of Zp is called rainbow–free with respect to a certain equation, if it contains no rainbow solution of the equation, that is, a solution whose elements have pairwise distinct colors. In this paper we describe the structure of rainbow–free 3–colorings of Zp with respect to all linear(More)
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