The Etzion-Silberstein conjecture holds for every Ferrers diagram if and only if it holds for the irreducible ones, which are precisely the integer points of integral polytopes in R^{2d-3} for each d.
The On-Line Encyclopedia of Integer Sequences
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Benjamini-Schramm convergent tree sequences have subtree entropy converging to a limit depending only on the limit object, and subtree density converging when long paths are excluded; both are dense in [0,1] for trees and series-reduced trees.
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Irreducible Ferrers diagrams in the Etzion-Silberstein conjecture
The Etzion-Silberstein conjecture holds for every Ferrers diagram if and only if it holds for the irreducible ones, which are precisely the integer points of integral polytopes in R^{2d-3} for each d.
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Benjamini-Schramm convergence and subtrees of trees
Benjamini-Schramm convergent tree sequences have subtree entropy converging to a limit depending only on the limit object, and subtree density converging when long paths are excluded; both are dense in [0,1] for trees and series-reduced trees.