Alexander Wires
Published 2019-07-31Version 1
We investigate the complexity of the partial order relation of Young's lattice. The definable relations are characterized by establishing the maximal definability property modulo the single automorphism given by conjugation; consequently, as an ordered set Young's lattice has an undecidable elementary theory and is inherently non-finitely axiomatizable but every ideal generates a finitely axiomatizable universal class of equivalence relations. We end with conjectures concerning the complexities of the $\Sigma_1$ and $\Sigma_2$-theories.
On the Complexity of Polytope Isomorphism Problems
On the Complexity of the Cogrowth Sequence
The complexity of the $q$-analog of the $n$-cube
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