Families of finite sets in which no set is covered by the union of the others
| Autor: | Guillermo Alesandroni |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Examples and Counterexamples, Vol 3, Iss , Pp 100095- (2023) |
| Druh dokumentu: | article |
| ISSN: | 2666-657X |
| DOI: | 10.1016/j.exco.2022.100095 |
| Popis: | Let ℱ be a finite nonempty family of finite nonempty sets. We prove the following: (1) ℱ satisfies the condition of the title if and only if for every pair of distinct subfamilies {A1,…,Ar}, {B1,…,Bs}of ℱ, ⋃i=1rAi≠⋃i=1sBi. (2) If ℱ satisfies the condition of the title, then the number of subsets of ⋃A∈ℱAcontaining at least one set of ℱ is odd. We give two applications of these results, one to number theory and one to commutative algebra. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
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