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- W4301688077 abstract "The Union Closed Sets Conjecture states that in every finite, nontrivial set family closed under taking unions there is an element contained in at least half of all the sets of the family. We investigate two new directions with respect to the conjecture. Firstly, we investigate the frequencies of all elements among a union closed family and pose a question generalizing the Union Closed Sets Conjecture. Secondly, we investigate structures equivalent to union closed families and obtain a weakening of the Union Closed Sets Conjecture. We pose some new open questions about union closed families and related structures and hint at some further directions of research regarding the conjecture." @default.
- W4301688077 created "2022-10-05" @default.
- W4301688077 creator A5057009924 @default.
- W4301688077 date "2022-08-07" @default.
- W4301688077 modified "2023-09-26" @default.
- W4301688077 title "Notes on the Union Closed Sets Conjecture" @default.
- W4301688077 doi "https://doi.org/10.48550/arxiv.2208.03803" @default.
- W4301688077 hasPublicationYear "2022" @default.
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