1 citations · 1 across the 4 of their papers we have counts for
4 papers
A Cantor-Bendixson Rank for Siblings of Trees
Davoud Abdi
Similar to topological spaces, we introduce the Cantor-Bendixson rank of a tree by repeatedly removing the leaves and the isolated vertices of using transfinite recursion.…
On Infinitely Many Siblings for Locally Finite Trees with Parabolic Embeddings
Davoud Abdi
Parabolic (resp. hyperbolic) self-embeddings of trees are those which do not fix a non-empty finite subtree and preserve precisely one (resp. two) end(s). We prove that a locally f…
A Proof of the Alternate Thomassé Conjecture for Countable -Free Posets
Davoud Abdi
An -free poset is a poset whose comparability graph does not embed an induced path with four vertices. We use the well-quasi-order property of the class of countable -free po…
Siblings of Direct Sums of Chains
Davoud Abdi
We prove that a countable direct sum of chains has either one, countably many or else continuum many isomorphism classes of siblings. This proves Thomassé's conjecture for such str…