8 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…

Conjecture on $C_k$. One has $C_k>0$ for every natural number $k$; moreover, $C_k$ is strictly decreasing as a function of $k$ for $k\geq 3$, and

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…

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

Let $k$ be an integer with $k\geq 3$, and define … Assign each $x_{i,j}$ to a formal variable from $\{c_1,\ldots,c_r\}$, subject to the condition that for every…

Let $k$ be a positive integer, and let the trigonometric constructs discussed in the paper be the finite sums arising from powers of circulant boolean matrices, including sums of t…

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…

For nonnegative integers $a_1,\dots,a_k$, define the multinomial coefficient … A $k$-nomial coefficient has weight $a_1+\dots+a_k$ and is proper when none of its arguments is zero.…