منابع مشابه
Monochromatic Sums Equal to Products in N
Csikvári, Gyarmati, and Sárközy asked whether, whenever the set N of positive integers is finitely colored, there must exist monochromatic a, b, c, and d such that a + b = cd and a �= b. We provide an affirmative answer, showing that a much stronger statement is true.
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Given graphs G and H, a vertex coloring c : V (G) → N is an H-free coloring of G if no color class contains a subgraph isomorphic to H. The H-free chromatic number of G, χ(H,G), is the minimum number of colors in an H-free coloring of G. The H-free chromatic sum of G, Σ(H,G), is the minimum value achieved by summing the vertex colors of each H-free coloring of G. We provide a general bound for ...
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Abstract: In this paper, we exhibit new conditions for the sum of two commuting AC-operators to be again an AC-operator. In particular, this is satisfied on Hilbert space when one of them is a scalar-type spectral operator.
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We study the sums of products of power sums of positive integers and their generalizations, using the multiple products of their exponential generating functions. The generalizations include a closed form expression for the sums of products of infinite series of the form ∑∞ n=0 α n, 0 < |α| < 1, k ∈ N0 and the related Abel sum, which define, in a unified way, the sums of products of the power s...
متن کاملPartitions and Sums and Products of Integers
The principal result of the paper is that, if r < u and (A¡)i<r is a partition of u, then there exist i < r and infinite subsets B and C of to such that 2 F e A¡ and IIG G A¡ whenever F and G are finite nonempty subsets of B and C respectively. Conditions on the partition are obtained which are sufficient to guarantee that B and C can be chosen equal in the above statement, and some related fin...
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ژورنال
عنوان ژورنال: Discrete Analysis
سال: 2016
ISSN: 2397-3129
DOI: 10.19086/da.613