D denotes the homomorphism poset of finite directed graphs. An antichain duality is a pair 〈F ,D〉 of antichains of D such that (F→) ∪ (→D) = D is a partition. A generalized duality pair in D is an antichain duality 〈F ,D〉 with finite F and D. We give a simplified proof of the Foniok Nešetřil Tardif theorem for the special case D, which gave full description of the generalized duality pairs in D...

We address a supersaturation problem in the context of forbidden subposets. A family F of sets is said to contain the poset P if there is an injection i : P → F such that p ≤P q implies i(p) ⊂ i(q). The poset on four elements a, b, c, d with a, b ≤ c, d is called a butterfly. The maximum size of a family F ⊆ 2 that does not contain a butterfly is ( n bn/2c ) + ( n bn/2c+1 ) as proved by De Boni...

A binary poset code of codimension m (of cardinality 2n−m , where n is the code length) can correct maximum m errors. All possible poset metrics that allow codes of codimension m to be m-, (m − 1)-, or (m − 2)-perfect are described. Some general conditions on a poset which guarantee the nonexistence of perfect poset codes are derived; as examples, we prove the nonexistence of r-perfect poset co...

We study a poset N on the free monoid X∗ on a countable alphabet X. This poset is determined by the fact that its total extensions are precisely the standard term orders on X ∗. We also investigate the poset classifying degree-compatible standard term orders, and the poset classifying sorted term orders. For the latter poset, we give a Galois coconnection with the Young lattice.

The Dushnik-Miller dimension of a partially-ordered set P is the smallest d such that one can embed into product linear orders. We prove divisibility order on interval {1,…,n}, equal to (log⁡n)2(log⁡log⁡n)−Θ(1) as n goes infinity. similar bounds for 2-dimension in where poset isomorphic suborder subset lattice [d]. also an upper bound posets bounded degree and show (αn,n] Θα(log⁡n) α∈(0,1). At ...

The interval poset of a permutation catalogues the intervals that appear in its one-line notation, according to set inclusion. We study this poset, describing structural, characterizing, and enumerative properties.