István Tomon

On a conjecture of Füredi

Furedi conjectured that the Boolean lattice 2 n ] can be partitioned into ( n ? n / 2 ? ) chains such that the size of any two differs in at most one. In this paper, we prove that there is an absolute constant α ? 0.8482 with the following property: for every ? 0 , if n is sufficiently large, the Boolean lattice 2 n ] has a chain partition into ( n ? n / 2 ? ) chains, each of them of size between ( α - ? ) n and O ( n / ? ) .We deduce this result by looking at the more general setup of unimodal normalized matching posets. We prove that a unimodal normalized matching poset P of width w has a chain partition into w chains, each of size at most 2 | P | w + 5 , and it has a chain partition into w chains, where each chain has size at least | P | 2 w - 1 2 .

Partitioning the Boolean lattice into copies of a poset

Let

Induced Subgraphs With Many Distinct Degrees

P

Ramsey Graphs Induce Subgraphs of Many Different Sizes

be a poset of size

Improved bounds on the partitioning of the Boolean lattice into chains of equal size

2^k

Forbidden induced subposets of given height

that has a greatest and a least element. We prove that, for sufficiently large

On the Turán number of some ordered even cycles

n

On the Size of K-Cross-Free Families

, the Boolean lattice

The poset on connected graphs is Sperner

2^{[n]}

Tiling the Boolean lattice with copies of a poset

can be partitioned into copies of