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Average Set Size in Union-Closed Sets by Thu TRAN Dan is a document available to read on EtoBox.

This paper proves that for a union-closed collection of sets A, the average set size is at least 12 log2 (|A|). The theorem builds on the Union-Closed Sets Conjecture and is demonstrated through two lemmas that establish relationships between union-closed families and filters. The results indicate that the only sharp cases occur when A equals the power set of some subset of [n].

Author

Thu TRAN Dan

Language

EN