Combinatorially rich sets in partial semigroups

Arpita Ghosh; Neil Hindman

doi:10.1016/j.topol.2025.109406

Combinatorially rich sets in partial semigroups

Arpita Ghosh, Neil Hindman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

There are several notions of size for semigroups that have natural analogues for partial semigroups. Among these are thick, syndetic, central, piecewise syndetic, IP, J, and the more recently introduced notion of combinatorially rich, abbreviated CR. We investigate the notion of CR set for adequate partial semigroups, its relation to other notions, especially J sets, and some surprising differences among them.

Original language	English
Article number	109406
Journal	Topology and its Applications
Volume	369
DOIs	https://doi.org/10.1016/j.topol.2025.109406
State	Published - 1 Aug 2025

Bibliographical note

Publisher Copyright:
© 2025 Elsevier B.V.

Keywords

Combinatorially rich sets
Partial semigroups

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2025.109406

Cite this

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AB - There are several notions of size for semigroups that have natural analogues for partial semigroups. Among these are thick, syndetic, central, piecewise syndetic, IP, J, and the more recently introduced notion of combinatorially rich, abbreviated CR. We investigate the notion of CR set for adequate partial semigroups, its relation to other notions, especially J sets, and some surprising differences among them.

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KW - Partial semigroups

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Combinatorially rich sets in partial semigroups

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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