6 problems

For each diameter $d \geqslant 2$, let … be an optimal tristance anticode in ${\cal G}^{\text{\tiny\rm \FourStar}}_3$, where the parameters describe the edge truncations of the ass…

Let an optimal tristance anticode in the three-dimensional integer grid be a largest subset of $\mathbb{Z}^3$ having a prescribed tristance diameter. Symmetry conjecture. Optimal t…

Let $A_n(D)$ be the maximum cardinality of a subset $\mathcal F\subseteq\mathbb Z^n$ whose diameter in the anticode metric $d_{\mathrm a}$ is at most $D$. Let $S_{n,D}$ be the simp…

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…

Conjecture on optimal anticode structure. For any $n$, the optimal anticode of maximal distance $d-1$ has the above form. In particular,