Kleitman and Combinatorics: A Celebration

Sperner's Theorem and a Problem of Erdős, Katona and Kleitman

A central result in extremal set theory is the celebrated theorem of Sperner from 1928, which gives the size of the largest family of subsets of [n] not containing a 2-chain F1 ⊂ F2. Erdős extended this theorem to determine the largest family without a k-chain F1 ⊂ F2 ⊂ . . . ⊂ Fk. Erdős and Katona, followed by Kleitman, asked how many chains must appear in families with sizes larger than the c...

A celebration and a challenge.

www.sciencemag.org SCIENCE VOL 323 9 JANUARY 2009 179 COVER Charles Darwin, a few years after his Beagle voyage. Science’s celebration of his 200th birthday and the 150th anniversary of the publication of On the Origin of Species begins with a Review by Bowler (p. 223) and an Essay on the origins of life (p. 198), the start of a monthly series exploring evolution. See also the Editorial (p. 185...

On a combinatorial problem of Erds, Kleitman and Lemke

In this paper, we study a combinatorial problem originating in the following conjecture of Erdős and Lemke: given any sequence of n divisors of n, repetitions being allowed, there exists a subsequence the elements of which are summing to n. This conjecture was proved by Kleitman and Lemke, who then extended the original question to a problem on a zero-sum invariant in the framework of finite Ab...

Celebration.

The Association of Nurse Education is celebrating a day in which many of the aspirations of nurse education campaigners over 50 years have been fulfilled.

A celebration of life.