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:
“Families need families. Parents need to be parented. Grandparents, aunts, and uncles are back in fashion because they are necessary. Stresses on many families are out of proportion to anything two parents can handle.”
—T. Berry Brazelton (20th century)
“Religion is organized to satisfy and guide the soul—politics does the same thing for the body.”
—Joyce Cary (1888–1957)
“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)