Results 41 to 50 of about 9,377,044 (73)
A subset $S$ of the Boolean hypercube $\mathbb{F}_2^n$ is a sumset if $S = \{a + b : a, b\in A\}$ for some $A \subseteq \mathbb{F}_2^n$. Sumsets are central objects of study in additive combinatorics, featuring in several influential results.
Chen, Xi +4 more
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Algebraic Proof for the Geometric Structure of Sumsets
, 2011 We consider a finite set of lattice points and their convex hull. The author previously gave a geometric proof that the sumsets of these lattice points take over the central regions of dilated convex hulls, thus revealing an interesting connection ...
Jaewoo Lee
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Dimension growth for iterated sumsets [PDF]
, 2018 Jonathan M. Fraser was financially supported by a Leverhulme Trust Research Fellowship (RF-2016-500) and an EPSRC Standard Grant (EP/R015104/1). Douglas C. Howroyd was financially supported by the EPSRC Doctoral Training Grant (EP/N509759/1).
Howroyd, Douglas Charles +2 more
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Small sumsets in real numbers : a continuous 3k-4 theorem
, 2016 We prove a continuous Freiman's 3k-4 theorem for small sumsets in R by using some ideas from Ruzsa's work on measure of sumsets in R as well as some graphic representation of density functions of sets.
de Roton, Anne
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SUMSETS AND CARRIES IN CYCLIC GROUPS [PDF]
, 2015 This thesis studies some direct and inverse problems concerning sumsets in cyclic groups, with applications to the study of carries. First of all we prove a generalization of the classical Cauchy-Davenport inequality in finite cyclic groups, thus ...
F. Monopoli
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The polynomial method in additive combinatorics [PDF]
, 2009 330 páginas.-- 2000 Mathematical Subject Classification 11P70, 11B50, 11R27.This book collects the material delivered in the 2008 edition of the DocCourse in Combinatorics and Geometry which was devoted to the topic of additive combinatorics.
Gyula Károlyi +4 more
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Structure of polytopes associated to non-additive measures via toric ideals and Gröbner bases
Acuerdos Transfomativos CRUE 2025In this paper we study the geometrical structure of some polytopes appearing in the study of families of non-additive measures using toric ideals and Gröbner bases.
García Segador, Pedro +1 more
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Small sumsets in $\protect \mathbb{R}$: full continuous $3k-4$ theorem, critical sets
, 2018 International audienceWe prove a full continuous Freiman's 3k-4 theorem for small sumsets in R by using some ideas from Ruzsa's work on measure of sumsets in R as well as some graphic representation of density functions of sets.
Anne de Roton, de Roton, Anne
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On two new kinds of restricted sumsets
, 2022 Let $A_1,\ldots,A_n$ be finite subsets of an additive abelian group $G$ with $|A_1|=\cdots=|A_n|\ge2$. Concerning the two new kinds of restricted sumsets $$L(A_1,\ldots,A_n)=\{a_1+\cdots+a_n:\ a_1\in A_1,\ldots,a_n\in A_n,\ \text{and}\ a_i\not=a_{i+1} \ \
Sun, Zhi-Wei, Wang, Han
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Oracally Efficient Two-Step Estimation of Generalized Additive Model [PDF]
Generalized additive models (GAM) are multivariate nonparametric regressions for non-Gaussian responses including binary and count data. We propose a spline-backfitted kernel (SBK) estimator for the component functions.
Wolfgang Karl Härdle +2 more
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