6 problems

Kimberling's conjecture. The set $S$ consists precisely of those natural numbers $n$ for which this new expression is an integer.

Let $x$ be an irrational real number. Let $G_x$ be a context-free grammar that generates an infinite sequence of Dyck rationals $(s_i)_{i\in\mathbb{N}_{+}}$, and let…

Let $\mathcal{D}_{r_{\text{min}}}$ be the language of minimal Dyck-word representations, and consider augmenting its words with additional notation or productions. Finite-length re…

Exceptional three-antipalindrome conjecture. Every even natural number outside $E$ is the sum of at most $3$ antipalindromes.

Four-antipalindrome conjecture. Every even natural number is the sum of at most $4$ antipalindromes.

The length-restricted antipalindrome sum conjecture. Every even integer of length $n$, for $n$ odd and $n\geq 9$, is the sum of at most $10$ antipalindromes of length $n-3$.