Countable ultrahomogeneous antimatroids of convex dimension 2

Poly-Dimension of Antimatroids

A partial cube is a graph that can be isometrically embedded into a hypercube. In other words, a partial cube is a subgraph of a hypercube that preserves distances the distance between any two vertices in the subgraph is the same as the distance between those vertices in the hypercube. Partial cubes were first introduced by Graham and Pollak (Graham & Pollak, 1971) as a model for communication ...

Maximal Chains of Isomorphic Subgraphs of Countable Ultrahomogeneous Graphs

For a countable ultrahomogeneous graph G = 〈G, ρ〉 let P(G) denote the collection of sets A ⊂ G such that 〈A, ρ ∩ [A]〉 ∼= G. The order types of maximal chains in the poset 〈P(G) ∪ {∅},⊂〉 are characterized as: (I) the order types of compact sets of reals having the minimum nonisolated, if G is the Rado graph or the Henson graph Hn, for some n ≥ 3; (II) the order types of compact nowhere dense set...

Maximal Chains of Isomorphic Suborders of Countable Ultrahomogeneous Partial Orders

We investigate the poset 〈P(X) ∪ {∅},⊂〉, where X is a countable ultrahomogeneous partial order and P(X) the set of suborders of X isomorphic to X. For X different from (resp. equal to) a countable antichain the order types of maximal chains in 〈P(X) ∪ {∅},⊂〉 are characterized as the order types of compact (resp. compact and nowhere dense) sets of reals having the minimum non-isolated. 2000 Math...

Antimatroids and Convex Geometries – The fundamentals

The length of Artinian modules with countable Noetherian dimension

‎It is shown that‎ ‎if $M$ is an Artinian module over a ring‎ ‎$R$‎, ‎then $M$ has Noetherian dimension $alpha $‎, ‎where $alpha $ is a countable ordinal number‎, ‎if and only if $omega ^{alpha }+2leq it{l}(M)leq omega ^{alpha‎ +1}$, ‎where $ it{l}(M)$ is‎ ‎the length of $M$‎, ‎$i.e.,$ the least ordinal number such that the interval $[0‎, ‎ it{l}(M))$ cannot be embedded in the lattice of all su...