5 problems

Let $n$ be a positive integer, and let $G_{3,3n}$ denote the shuffle group on $3n$ cards generated by the standard shuffle and permutations of the three piles. Xia–Zhang–Zhu conjec…

Cohen–Harmse–Morrison–Wright conjecture. The shuffle group $G_{k,kn}$ contains the alternating group $A_{kn}$ if $k\geq3$, $(k,n)\neq\{4,2^f\}$ for any positive integer $f$, and…

For positive integers $k$ and $n$, let $G_{k,kn}$ be the group generated by the $k!$ permutations of a deck of $kn$ cards obtained by cutting it into $k$ piles of $n$ cards and per…

Let $k$ be an odd prime, let $n>k$, and suppose that $n$ is not a power of $k$. Cyclic-prime shuffle-group conjecture. Then … This is presented as a computationally verified expect…

Let $k\geqslant 3$ and let $n$ be a positive integer that is not a power of $k$; when $k=4$, also assume that $n\neq 2^f$ for every positive integer $f$. Write…