Poset game periodicity.
Poset homology of Rees products, and -Eulerian polynomials.
Posets having a selfdual interval poset
Posets having a unique decomposition into the minimum number of antichains. (Short Communication).
Posets having a unique decomposition into the minimum number of antichains.
Power-ordered sets
We define a natural ordering on the power set 𝔓(Q) of any finite partial order Q, and we characterize those partial orders Q for which 𝔓(Q) is a distributive lattice under that ordering.
Powers of partially ordered sets: Cancellation and reffinement properties.
Powers of partially ordered sets: The automorphism group.
Préfermeture sur un ensemble ordonné
Préordres et équivalences dans l'ensemble des familles d'un ensemble
Prime and maximal ideals of partially ordered sets
Prime elements in the semigroup of finite types of partially ordered sets in cardinal multiplication
Prime ideals in 0-distributive posets
In the first section of this paper, we prove an analogue of Stone’s Theorem for posets satisfying DCC by using semiprime ideals. We also prove the existence of prime ideals in atomic posets in which atoms are dually distributive. Further, it is proved that every maximal non-dense (non-principal) ideal of a 0-distributive poset (meet-semilattice) is prime. The second section focuses on the characterizations of (minimal) prime ideals in pseudocomplemented posets. The third section deals with the generalization...
Primeness and semiprimeness in posets
The concept of a semiprime ideal in a poset is introduced. Characterizations of semiprime ideals in a poset as well as characterizations of a semiprime ideal to be prime in are obtained in terms of meet-irreducible elements of the lattice of ideals of and in terms of maximality of ideals. Also, prime ideals in a poset are characterized.
Primes, coprimes and multiplicative elements
The purpose of this paper is to study conditions under which the restriction of a certain Galois connection on a complete lattice yields an isomorphism from a set of prime elements to a set of coprime elements. An important part of our study involves the set on which the way-below relation is multiplicative.
Products OF IDEMPOTENT ORDER-PRESERVING TRANSFORMATIONS OF ARBITRARY CHAINS.
Profile classes and partial well-order for permutations.
Promotion and evacuation.
Properties of monotone mappings in partially ordered sets.
Properties of relatively pseudocomplemented directoids
The concept of a relatively pseudocomplemented directoid was introduced recently by the first author. It was shown that the class of relatively pseudocomplemented directoids forms a variety whose axiom system contains seven identities. The aim of this paper is three-fold. First we show that these identities are not independent and their independent subset is presented. Second, we modify the adjointness property known for relatively pseudocomplemented semilattices in the way which is suitable for...