4 problems

Guruswami–Riazanov conjecture. For every $k>3$, the Fredman–Komlós bound can be improved exponentially; that is, perfect $k$-hashing codes satisfy an upper bound with a strictly sm…

For $k>6$, let $p$ and $q$ be the values specified in case $(a)$ of the paper's preceding case analysis, and let $R_k$ denote the rate parameter under discussion. Maximum conjectur…

Let $s_q$ denote the parameter studied in the paper for $q$-perfect hashing. For odd $q$, consider positive constants $c_1$ and $c_2$. Venkatesh's conjecture. There exist positive…

Let $k\geq 3$, let $x=(x_1,\dots,x_k)$ have nonnegative coordinates satisfying … and let $S_h^{k-1}(x)$ denote the $h$-th elementary symmetric sum of $x_1,\dots,x_{k-1}$. The conje…