Families Known To Satisfy The Conjecture
The conjecture has been proven for many special cases of union-closed set families. In particular, it is known to be true for
- families of at most 46 sets (Roberts & Simpson 2010).
- families of sets such that their union has at most 11 elements, and
- families of sets in which the smallest set has one or two elements.
Read more about this topic: Union-closed Sets Conjecture
Famous quotes containing the words families, satisfy and/or conjecture:
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—Gloria Steinem (b. 1934)
“The general review of the past tends to satisfy me with my political life. No man, I suppose, ever came up to his ideal. The first half [of] my political life was first to resist the increase of slavery and secondly to destroy it.... The second half of my political life has been to rebuild, and to get rid of the despotic and corrupting tendencies and the animosities of the war, and other legacies of slavery.”
—Rutherford Birchard Hayes (1822–1893)
“There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)