A study on some combinatorial sets in partial semigroups

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.

Updated version. 14 pages. Comments are welcome! arXiv admin note: text overlap with arXiv:1809.01960, and with arXiv:1810.05097 by other authors