# A study on some combinatorial sets in partial semigroups

## TL;DR

This paper explores the properties and relationships of key combinatorial sets like central sets and C-sets within partial semigroups, revealing new distinctions and behaviors under homomorphisms.

## Contribution

It introduces new results on the existence of C-sets that are not central in the context of partial semigroups, expanding understanding of their structure.

## Key findings

- Identified conditions under which C-sets are not central
- Analyzed the image and preimage of combinatorial sets under homomorphisms
- Proved new theorems on the existence of specific combinatorial sets

## Abstract

In this article, we investigate the image and preimage of the important combinatorial sets such as central sets, $C$-sets, and $J_\delta$-sets which play an important role in the study of combinatorics under certain partial semigroup homomorphism. Using that we prove certain results which deal with the existence of $C$-set which are not central in partial semigroup framework.