Profile classes and partial well-order for permutations.
Promotion and evacuation.
P-sets and minimal right ideals in ℕ*
Recall that a P-set is a closed set X such that the intersection of countably many neighborhoods of X is again a neighborhood of X. We show that if 𝔱 = 𝔠 then there is a minimal right ideal of (βℕ,+) that is also a P-set. We also show that the existence of such P-sets implies the existence of P-points; in particular, it is consistent with ZFC that no minimal right ideal is a P-set. As an application of these results, we prove that it is both consistent with and independent of ZFC that the shift...
Ramsey-type theorems
Rationality, irrationality, and Wilf equivalence in generalized factor order.
Sacks forcing collapses to
We shall prove that Sacks algebra is nowhere -distributive, which implies that Sacks forcing collapses to .
Semiorders and Riordan numbers.
Set families with a forbidden subposet.
Short Note: Counting Conjectures.
Shuffle-invariant total orders.
Sign-graded posets, unimodality of -polynomials and the Charney-Davis conjecture.
Some cardinal characteristics of ordered sets
For ordered (= partially ordered) sets we introduce certain cardinal characteristics of them (some of those are known). We show that these characteristics—with one exception—coincide.
Some Geometric Applications of Dilworth's Theorem.
Some properties of Eulerian lattices
In this paper, we prove that Eulerian lattices satisfying some weaker conditions for lattices or some weaker conditions for 0-distributive lattices become Boolean.
Sortable elements for quivers with cycles.
Splitting numbers of grids.
Standard paths in another composition poset.
Sunflowers in lattices.
Sur le nombre d'éléments des niveaux des produits de chaînes et des treillis permutoèdres
Les produits de chaînes comptent parmi les ensembles (partiellement) ordonnés les plus fréquemment rencontrés. On rappelle, avec des démonstrations en partie nouvelles, divers résultats exacts ou approchés sur les cardinaux de leurs niveaux et sur le nombre de ses niveaux de cardinal maximum. Un plongement avec de bonnes propriétés permet d'appliquer ces résultats aux niveaux du permutoèdre (ordre faible de Bruhat sur les permutations).
The action of the symmetric group on a generalized partition semilattice.