Quadratic bound conjecture for the pair-matching decomposition number

Let H=(V,E)H=(V,E) be a 33-uniform hypergraph with nn vertices. Quadratic bound conjecture. Its pair-matching decomposition number satisfies

pmd(H)32n2152n+10.\operatorname{pmd}(H)\leq \frac{3}{2}n^2-\frac{15}{2}n+10.

This bound would follow from the preceding positive-matching conjecture and would give bounds for the irreducibility of coordinate sections of symmetric tensor varieties. The source states it as an unproved conjecture.

Sources & referencesView supporting material

Primary source

Shekoofeh Gharakhloo and Volkmar Welker, “Hypergraph LSS-ideals and coordinate sections of symmetric tensors”, arXiv:2202.10463 (2022).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.