Alex Wires, Department of Pure Mathematics, University of Waterloo
“Complexity of Young’s Lattice”
Young’s Lattice is the poset of integer partitions ordered according to inclusion of their Ferrers diagrams. It appears to be well-behaved since partitions enjoy various notions of Reconstruction (Pretzel, Siemons), but nuanced, as certain subposets have dihedral symmetry (Suter). How complicated is the lattice ordering? We describe the scope of definable sets and find it is as complicated as we can reasonably expect when we encounter second-order arithmetic.
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