Problems
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Must every r-differential poset have at least as many elements in each rank as Y^r, the r-th Cartesian power of Young's lattice? For r = 3 the new construction has fourth-rank size 50 against 51 for Y^3.
At the conjectured density, must every k-uniform hypergraph contain a short nontrivial even cover - a set of hyperedges covering each vertex an even number of times - with no superfluous polylogarithmic factors? Known up to polylog factors…
Let H be a hypertree. Then X_H is F-positive.
For every K_r -free graph G, fracα(G)overlineα_G(1)≥ 1+1/r. For every K_r -free graph G of minimum degree d, fracα(G)overlineα_G(1)≥ 2-o_d(1), with r fixed as d →∞ .