5 problems

Let an $(n,m,d)$-array be a set of strings of length $n$ over an alphabet of size $m$, with pairwise Kendall-$\tau$ distance at least $d$, and let $P(n,d)$ denote the relevant maxi…

Super-long-snake conjecture. There exists a $(2n+1,M_{2n+1},\mathcal{K})$-snake with

Longer-snake conjecture. There exists a $(2n+1,M_{2n+1},\mathcal{K})$-snake with

Let $S_n$ be the symmetric group on $n$ elements, equipped with Kendall's $\tau$-distance. Let $e=[1,2,\ldots,n]$ be the identity permutation, and let ${\cal S}(e,R)$ be the sphere…

Let $S_n$ be the symmetric group on $n$ elements, equipped with Kendall's $\tau$-distance. An anticode is a subset of $S_n$ whose maximum pairwise Kendall's $\tau$-distance is boun…