5 problems

Let $I_n^D$ denote the involutions in the type-D signed permutation group, and let $G({\mathcal S}_n^B,X_1^D\cup X_2^D)$ be the Cayley graph with generating sets … … Consider the r…

Let $\mathcal{W}_{q,n}$ denote the set of restricted binary words of length $n$ associated with the positive rational parameter $q$. A 1-Gray code is an arrangement of all words in…

Let $n\geq 0$ and $q\geq 1$, and let $\mathcal{W}^q_n$ denote the set of Fibonacci $q$-decreasing words of length $n$. A 1-Gray code for $\mathcal{W}^q_n$ is an ordering of its wor…

Let $Q_n$ be the $n$-dimensional hypercube, and let $Q_{n,[a,b]}$ denote the subgraph induced by the vertices whose levels lie in $[a,b]$. For integers $k\geq 1$ and…

4-adjacent Gray code conjecture. The resulting list is a $4$-adjacent Gray code.