3 problems

Let $\Sigma=\{\mathtt{a},\mathtt{b}\}$, let $w^R$ denote reversal, and let $\operatorname{ScatFact}_k(w)$ be the set of length-$k$ scattered factors of $w$. Consider the binary…

Let $k$ be a positive integer, and consider the cardinalities of $k$-spectra $\operatorname{ScatFact}_k(w)$ of strictly balanced binary words of length $2k$. The first gap is the i…

Let $\Sigma=\{\mathtt{a},\mathtt{b}\}$, and let $\Sigma_{sb}^{n}$ denote the strictly balanced words of length $n$. For a word $w$, write $\operatorname{ScatFact}_k(w)$ for its set…