On the exterior algebra method applied to restricted set addition

On Restricted Set Addition in Abelian Groups

Let A be a set of k elements of an Abelian group G in which the order of the smallest nonzero subgroup is at least 2k − 3. Then the number of different elements of G that can be written in the form a + a′, where a, a′ ∈ A, a 6= a′, is at least 2k − 3, as it has been shown in [12]. Here we give yet another proof of this result.

Numerical exterior algebra and the compound matrix method

Restricted Set Addition in Groups, I. the Classical Setting

We survey the existing and prove several new results for the cardinality of the restricted doubling 2̂ A = {a′+a′′ : a, a ∈ A, a 6= a′′}, where A ⊆ G is a subset of the set of elements of an (additively written) group G. In particular, we improve known estimates for G = Z and G = Z/pZ and give a first-of-a-kind general estimate valid for arbitrary G. 1. Background, motivation and summary of resu...

on the status of mixed methods research in applied linguistics

چکیده ندارد.

Restricted set addition in Abelian groups : results and conjectures par

We present a system of interrelated conjectures which can be considered as restricted addition counterparts of classical theorems due to Kneser, Kemperman, and Scherk. Connections with the theorem of Cauchy-Davenport, conjecture of ErdősHeilbronn, and polynomial method of Alon-Nathanson-Ruzsa are discussed. The paper assumes no expertise from the reader and can serve as an introduction to the s...