5 problems

Let $M(n)$ denote the number of distinct multinomial coefficients arising from partitions of $n$. Exact-asymptotic-constant conjecture. … The paper explains that this would follow…

Let $M(n)$ denote the number of distinct multinomial coefficients arising from partitions of $n$. Asymptotic-growth conjecture. There exists a positive constant $C$ such that … Thi…

Let $M(n)$ be the number of distinct multinomial coefficients arising from partitions of $n$, and let $p^*(n)$ be the total number of partitions of $n$ into parts that are either a…

Monotonicity conjecture for $S_3^{(3)}$. The sequence

For integers $m,n\geq 1$ and $r\geq 0$, define the multinomial power sums … where $k_1,\ldots,k_m\geq 0$ and $k_1+\cdots+k_m=n$. The multinomial congruence conjecture. Let…