7 problems

Let $(X,\mathcal B)$ be a cyclic $(v,k,1)$-BIBD, and partition its blocks into orbits under the cyclic automorphism. Call a fixed block from each orbit a base block. Feng–Horsley–W…

Let $k$ and $\lambda$ be fixed positive integers with $k\geqslant \lambda+1$. Let $(X,\mathcal B)$ be a cyclic $(v,k,\lambda)$-BIBD with $v\geqslant v_0$, where $v_0$ is an integer…

KSWX conjecture. Whenever $x$ is a prime power, there exists a cyclic difference family with the parameter set $$ and multiplier

Cyclic design existence conjecture. Cyclic $(v,4,1)$-designs exist for all $v\equiv 1,4\pmod{12}$ and $v\geqslant 37$.

Let $k$ and $\lambda$ be fixed positive integers with $k\geqslant\lambda+1$, and let $(V,\mathcal{B})$ be a cyclic $(v,k,\lambda)$-design. A base block is one chosen block from eac…

Let $(V,\mathcal{B})$ be a cyclic $(v,k,1)$-design: the blocks are partitioned into orbits under a cyclic automorphism, and a base block is one chosen block from each orbit. Disjoi…

Let $T$ be a tree with $n+1$ vertices, and identify the vertices of $K_{2n+1}$ with the integers modulo $2n+1$. A cyclic decomposition into copies of $T$ consists of the cyclic shi…