New York Journal of Mathematics
Volume 30 (2024), 38-41


Pintu Debnath and Sayan Goswami

Combined exponential patterns in multiplicative IP* sets

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Published: January 16, 2024.
Keywords: Algebra of the Stone-Cech compactification, exponential patterns, multiplicative IP* set.
Subject [2020]: 54D35, 05D10, 54H15.

In this article we prove that multiplicative IP* sets contain two different exponential patterns and a finite product of a single sequence. This immediately improves the result of A. Sisto [4], where he proved that multiplicative IP* sets contain different exponential patterns for different sequences. Throughout our work we will use the machinery of the Algebra of the Stone-Čech Compactification of N.


We are thankful to Sourav Kanti Patra for discussions in several occasions. We are also thankful to the referee for his/her comments on the previous draft of this paper.

Author information

Pintu Debnath
Department of Mathematics
Basirhat College
Basirhat 743412, North 24th parganas
West Bengal, India


Sayan Goswami
The Institute of Mathematical Sciences
A CI of Homi Bhabha National Institute, CIT Campus
Taramani, Chennai 600113, India