Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An old problem of Moser asks: what is the size of the largest union-free subfamily that one can guarantee in every family of m sets? A family of sets is called union-free if there are no three distinct sets in the family such that the union of two of the sets is equal to the third set.  show that every family of m sets contains a union-free subfamily of size at least \(\left\lfloor {\sqrt {4m + 1} } \right\rfloor - 1\) and that this bound is tight. This solves Moser’s problem and proves a conjecture of Erdős and Shelah from 1972.
['Jacob Fox', 'Choongbum Lee', 'Benny Sudakov']
I am writing a research paper on a idea Maximum union-free subfamilies
[{"from": "human", "value": "I am writing a research paper on a idea Maximum union-free subfamilies"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An old problem of Moser asks: what is the size of the largest union-free subfamily that one can guarantee in every family of m sets? A family of sets is called union-free if there are no three distinct sets in the family such that the union of two of the sets is equal to the third set.  show that every family of m sets contains a union-free subfamily of size at least \\(\\left\\lfloor {\\sqrt {4m + 1} } \\right\\rfloor - 1\\) and that this bound is tight. This solves Moser\u2019s problem and proves a conjecture of Erd\u0151s and Shelah from 1972."}]