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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
3
votes
Does the rank (=height) of a well partial order bound its type (=length, =stature)?
The height (aka rank) and maximal order type (aka type, aka length, aka stature) of a wpo are not functionally related.
Consider for instance the family of finite partial orders (thus wpos) $P_n=\{a_ …
3
votes
Accepted
A variant of Kruskal's theorem
To reformulate your question, given a wqo $(A,\leq)$, here finite trees with the minor ordering, you ask whether $({\mathcal P}_\mathrm{fin}(A),\sqsubseteq)$ the set of finite subsets of $A$ with a `m …