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Search: All articles in the CJM digital archive with keyword additive

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1. CJM Online first

Green, Ben Joseph; Lindqvist, Sofia
Monochromatic solutions to $x + y = z^2$
Suppose that $\mathbb{N}$ is $2$-coloured. Then there are infinitely many monochromatic solutions to $x + y = z^2$. On the other hand, there is a $3$-colouring of $\mathbb{N}$ with only finitely many monochromatic solutions to this equation.

Keywords:additive combinatorics, Ramsey theory
Categories:11B75, 05D10

2. CJM 2015 (vol 68 pp. 44)

Fernández Bretón, David J.
Strongly Summable Ultrafilters, Union Ultrafilters, and the Trivial Sums Property
We answer two questions of Hindman, Steprāns and Strauss, namely we prove that every strongly summable ultrafilter on an abelian group is sparse and has the trivial sums property. Moreover we show that in most cases the sparseness of the given ultrafilter is a consequence of its being isomorphic to a union ultrafilter. However, this does not happen in all cases: we also construct (assuming Martin's Axiom for countable partial orders, i.e. $\operatorname{cov}(\mathcal{M})=\mathfrak c$), on the Boolean group, a strongly summable ultrafilter that is not additively isomorphic to any union ultrafilter.

Keywords:ultrafilter, Stone-Cech compactification, sparse ultrafilter, strongly summable ultrafilter, union ultrafilter, finite sum, additive isomorphism, trivial sums property, Boolean group, abelian group
Categories:03E75, 54D35, 54D80, 05D10, 05A18, 20K99

3. CJM 2010 (vol 63 pp. 222)

Wang, Jiun-Chau
Limit Theorems for Additive Conditionally Free Convolution
In this paper we determine the limiting distributional behavior for sums of infinitesimal conditionally free random variables. We show that the weak convergence of classical convolution and that of conditionally free convolution are equivalent for measures in an infinitesimal triangular array, where the measures may have unbounded support. Moreover, we use these limit theorems to study the conditionally free infinite divisibility. These results are obtained by complex analytic methods without reference to the combinatorics of c-free convolution.

Keywords:additive c-free convolution, limit theorems, infinitesimal arrays
Categories:46L53, 60F05

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