7 problems

Let $[n]=\{1,\ldots,n\}$, and let a Universal Cycle for $t$-multisets of $[n]$ be a cyclic sequence of $\binom{n+t-1}{t}$ integers from $[n]$ in which every $t$-multiset of $[n]$ a…

Compatibility conjecture. $\mathfrak S$ is compatible if and only if every submultiset of $\mathfrak S$ of size at most $\Delta(\mathcal M)+2$ is compatible.

Let $s>2$ and $n>2s$, and let an $n$-multiset be a multiset with $n$ elements. Two $n$-multisets are $s$-equivalent when they have the same multiset of $s$-sums. Magical Triplet Co…

Let $F_{s,k}(n)$ be the Moser polynomial, and let $k_{\max}(s)$ denote the largest positive integer $k$ for which $F_{s,k}$ has an integer root. $k_{\max}$-conjecture. For all…

Let $k,n,t$ be positive integers with $t\leq k$, let $M(n,k)$ be the rectangle representation of $k$-multisets, and let $\mathcal{M}(n,k,t)$ denote the families of $t$-intersecting…

Let $[n]=\{1,\ldots,n\}$, let $M(n,k)$ be the $k\times n$ rectangle representation of $k$-multisets, and let $\mathcal{M}(n,k,t)$ denote the families of $t$-intersecting $k$-multis…

Let $[n]=\{1,\ldots,n\}$, and let a $k$-multiset on $[n]$ be a multiset of cardinality $k$ whose elements lie in $[n]$. Two multisets are $t$-intersecting when their intersection h…