Math 249: Algebraic Combinatorics
نویسندگان
چکیده
منابع مشابه
Covering the Large Spectrum and Generalized Riesz Products
Chang’s Lemma is a widely employed result in additive combinatorics. It gives optimal bounds on the dimension of the large spectrum of probability distributions on nite abelian groups. In this note, we show how Chang’s Lemma and a powerful variant due to Bloom both follow easily from an approximation theorem for probability measures in terms of generalized Riesz products. The latter result invo...
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An arc in a tournament T with n ≥ 3 vertices is called pancyclic if it belongs to a cycle of length l for all 3 ≤ l ≤ n. We call a vertex u of T an out-arc pancyclic vertex of T if each out-arc of u is pancyclic in T . Yao, Guo and Zhang [Discrete Appl. Math. 99 (2000), 245–249] proved that every strong tournament contains at least one out-arc pancyclic vertex, and they gave an infinite class o...
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Consider a pair of group divisible designs (GDD) with block size 3, index λ = 1, and on the same points and groups. They are said to be orthogonal (OGDD) if (i) whenever two blocks, one from each design, intersect in two points, the third points are in different groups; and (ii) two disjoint pairs of points defining intersecting triples in one GDD fail to do so in the other. A question posed by...
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