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The $ n $-cube is the poset obtained by ordering all subsets of $\{1,\ldots, n\} $ by inclusion,
and it can be partitioned into $\binom {n}{\lfloor n/2\rfloor} $ chains, which is the minimum …

Let P be a partially ordered set. The function La⁎(n, P) denotes the size of the largest family
F⊂ 2 [n] that does not contain an induced copy of P. It was proved by Methuku and Pálvölgyi …

The central levels problem asserts that the subgraph of the (2 m+ 1)-dimensional hypercube
induced by all bitstrings with at least m+ 1− ℓ many 1s and at most m+ ℓ many 1s, ie, the …

Consider the partially ordered set on $[t]^ n:=\{0,\dots, t-1\}^ n $ equipped with the natural
coordinate-wise ordering. Let $ A (t, n) $ denote the number of antichains of this poset. The …

The Boolean lattice is the family of all subsets of ordered by inclusion, and a chain is a family
of pairwise comparable elements of. Let, which is the average size of a chain in a minimal …

The Boolean lattice 2 [n] is the power set of [n] ordered by inclusion. If c is a positive integer,
a c-partition of a poset is a chain partition, where all but at most one of the chains have size …

The Boolean lattice $2^{[n]} $ is the power set of $[n] $ ordered by inclusion. A chain $ c_
{0}\subset...\subset c_ {k} $ in $2^{[n]} $ is rank-symmetric, if $| c_ {i}|+| c_ {ki}|= n $ for $ i …

In this short paper, we prove the following generalization of a result of Methuku and P\'{a}
lv\"{o} lgyi. Let $ P $ be a poset, then there exists a constant $ C_ {P} $ with the following …

The n-cube is the poset obtained by ordering all subsets of 11,..., nl by inclusion, and it can
be partitioned into ( n⌊ n/2⌋) chains, which is the minimum possible number. Two such …