Asymmetric infinite sumsets in large sets of integers

Key Points

• The study investigates the existence of infinite asymmetric sumsets within large integer sets with specific density conditions.
• Defined set A with positive upper density.
• Constructed infinite set B using pairwise combinations of integer elements.
• Analyzed configurations under different density criteria and shifts.
• Confirmed a conjecture regarding infinite sets in integers.
• Demonstrated that sets with lower density > 1/2 include infinite configurations up to a shift.
• Established that the threshold of 1/2 is optimal for density considerations.