6 problems

Let $\gamma_k^B$ denote the Bernoulli matching-model limiting constant for alphabet size $k$. Boutet de Monvel's conjecture. … The source presents this as a conjecture about the as…

For alphabet size $k$, let $\gamma_k^B$ be the Bernoulli matching-model limiting constant and let $\gamma_k$ be the corresponding random-string-model limiting constant. Equality co…

Boutet de Monvel's conjecture. The Bernoulli matching-model growth constant satisfies the displayed formula. Boutet de Monvel also gave a more general conjecture for off-diagonal l…

Let $\mathcal{P}_k$ be the set of permutations of $[k]$, and let an arbitrary probability distribution be given on $\mathcal{P}_k$. Sample $\pi_1,\pi_2$ independently from this dis…

Beame and Huynh-Ngoc's conjecture. For every $k$ that is a power of $2$, this bound is tight up to a multiplicative constant; equivalently, there is a constant depending on $k$ suc…

Let $L_{n,\sigma,d}$ be the length of a longest common subsequence of $d$ sequences of length $n$, whose characters are chosen uniformly and independently from an alphabet of size…