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Restricted sumset. In additive number theory and combinatorics, a restricted sumset has the form. where are finite nonempty subsets of a field F and is a polynomial over F. If is a constant non-zero function, for example for any , then is the usual sumset which is denoted by if. When. S is written as which is denoted by if.
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Restricted sumset. Sidon set. Sum-free set. Schnirelmann...
- Sumset
Restricted sumset. Sidon set. Sum-free set. Schnirelmann density. Shapley–Folkman lemma. X + Y sorting. References. Henry Mann (1976). Addition Theorems: The Addition Theorems of Group Theory and Number Theory (Corrected reprint of 1965 Wiley ed.). Huntington, New York: Robert E. Krieger Publishing Company. ISBN 0-88275-418-1.
20 de set. de 2022 · In this chapter, we present literature survey on sumsets of different types including sum of dilated set of integers, h-fold sumset, restricted h-fold sumset, h-fold signed sumset, and restricted h-fold signed sumset. We also present an extensive survey on sumsets in different groups and pose some research directions.
Definition 1. A set A of integers is said to be restricted-sum-dominant if. | +A| > |A A|. There are examples of this. For example, we find the set from Hegarty [3] A15 = {0, 1, 2, 4, 5, 9, 12, 13, 17, 20, 21, 22, 24, 25, 29, 32, 33, 37, 40, 41, 42, 44, 45} has |A15 +A15| ˆ = 86 whilst |A15 A15| = 83.
23 de nov. de 2023 · As in the case of sumsets of sets, if \ (\mathscr {A}_i = \mathscr {A}\) for all \ (i = 1, \ldots , h\), then we denote the multisumset \ (\mathscr {A}_1 \hat {+} \cdots \hat {+} \mathscr {A}_h\) by \ (h~\hat {}\mathscr {A}\), and call this the restricted h - fold multisumset of \ (\mathscr {A}\).
20 de fev. de 2022 · Restricted sumsets - the origins? Ask Question. Asked 2 years, 1 month ago. Modified 2 years, 1 month ago. Viewed 113 times. 2. The sumset of the subsets A A and B B of an additively written group is defined by A + B:= {a + b: a ∈ A, b ∈ B} A + B := { a + b: a ∈ A, b ∈ B }. The basic idea to add sets has been around since Cauchy at least.
Now let H be a given finite set of nonnegative integers. Define the sumset [1, p. 175] HA:= [h∈H hA, and the restricted sumset HˆA:= [h∈H hˆA. Here we are assuming that 0A= 0ˆA= {0}. For a set Aand for an integer c, we let c·A= {ca: a∈ A}. For integers a,bwith a≤ b, we also let [a,b] = {a,a+1,...,b}.
