Recent progress in subset combinatorics of groups
Abstract
We systematize and analyze some results obtained in Subset Combinatorics of groups after publications the previous surveys [1-4]. The main topics: the dynamical and descriptive characterizations of subsets of a group relatively their combinatorial size, Ramsey-product subsets in connection with some general concept of recurrence in -spaces, new ideals in the Boolean algebra of all subsets of a group and in the Stone-ech compactification of , the combinatorial derivation.
Cite
@article{arxiv.1802.04106,
title = {Recent progress in subset combinatorics of groups},
author = {Igor Protasov and Ksenia Protasova},
journal= {arXiv preprint arXiv:1802.04106},
year = {2018}
}
Comments
Large, small, thin, thick, sparse and scattered subsets of groups; descriptive complexity; Boolean algebra of subsets of a group; Stone-$\check{C}$ech compactification; ultracompanion; Ramsey-product subset of a group; recurrence; combinatorial derivation. arXiv admin note: text overlap with arXiv:1704.02494