Exponentiations of ultrafilters
Combinatorics
2025-04-02 v5
Abstract
In recent years, several problems regarding the partition regularity of exponential configurations have been studied in the literature, in some cases using the properties of specific ultrafilters. In this paper, we start to lay down the foundations of a general theory of exponentiations of ultrafilters, with a particular focus on their combinatorial properties and the existence of idempotents.
Cite
@article{arxiv.2308.02807,
title = {Exponentiations of ultrafilters},
author = {Lorenzo Luperi Baglini},
journal= {arXiv preprint arXiv:2308.02807},
year = {2025}
}
Comments
This is part of a previous preprint, written together with Sayan Goswami and Sourav Kanti Patra, that we decided to split to make each of them more focused on specific aspects of the partition regularity of exponentiation. The other part of the previous preprint can be found here: arXiv:2411.19606