8 problems

Multiplicative monotonicity conjecture. Is

Let $t(n)$ be the maximum number of transpositions needed to sort a circular permutation of size $n$. Circular sorting monotonicity question. Is … for all values of $n$? Adding an…

Let $t(n)$ be the maximum, over circular permutations of size $n$, of the minimum number of transpositions needed to sort them. Drop-four circular sorting problem. Is there a value…

Let $t(n)$ be the maximum, over permutations of $\mathbb{Z}_n$ modulo cyclic shifts, of the minimum number of transpositions needed to sort the resulting circular permutation. Prim…

Let $S(\mathbb{Z}_n)$ denote the permutations of $\mathbb{Z}_n$, let $[\pi]$ be the coset of a permutation $\pi$ under cyclic shifts, and let $t([\pi])$ be the minimum number of tr…

Let $S(\mathbb{Z}_n)$ denote the permutations of $\mathbb{Z}_n$, let $[\pi]$ be the coset of a permutation $\pi$ under cyclic shifts, and let $t([\pi])$ be the minimum number of tr…

NP-hardness conjecture. The repeated-round Dealer's choice pile shuffle sort problem is NP-hard.

Consider a labeled chip-firing process on a graph in which each pair of adjacent sites is connected by $r$ edges and each site has $r$ self-loops. A firing move chooses $3r$ chips…