3 problems

Let $Y_{(1)}$ be the largest box size in the random allocation, and suppose $0<\nu<\lambda$. Nonvanishing maximum-size subsequence conjecture. There exists $\varepsilon>0$ and a su…

Let $Y_{(j)}$ be the $j$th largest box size in the conditioned allocation, and let $\xi_{(j)}$ be the $j$th largest observation in the corresponding independent reference sample. W…

Let $\mathbf{w}=(w_k)_{k\geqslant0}$ be a weight sequence with radius parameter $\rho>0$. Let $Y_{(1)}$ denote the largest box size in the associated random allocation, with…