2 problems

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The general equality conjecture for $H(m,\alpha)$ and $H_2(m,\alpha)$
General equality conjecture.
Conjectureopenextremal-combinatorics forbidden-configurations matrix-avoidancearXiv posted 2 days ago
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The equality conjecture for $H(m,2)$ and $H_2(m,2)$
Let $H(m,2)$ and $H_2(m,2)$ denote the two quantities defined in the paper for integers $m\geq 3$ . Equality conjecture. … Consequently, the paper's forbidden-configuration function…
Conjectureopenextremal-combinatorics forbidden-configurations matrix-avoidancearXiv posted 2 days ago

The general equality conjecture for H(m,α)H(m,\alpha)H(m,α) and H2(m,α)H_2(m,\alpha)H2​(m,α)