The kaon–glide positivity conjecture

A weak composition is a finite sequence of nonnegative integers. For weak compositions $a$ and $b$, let $\overline{\mathfrak{P}}_a$ denote the kaon associated with $a$, and let $\overline{\mathfrak{F}}_b$ denote the glide polynomial associated with $b$. Kaon–glide positivity conjecture. For any weak compositions $a$ and $b$, the product

$$\overline{\mathfrak{P}}_a\cdot\overline{\mathfrak{F}}_b$$

expands as a positive sum of kaons. This is a proposed positive structure theorem for the $K$-theoretic kaon basis, whose individual structure coefficients need not otherwise be positive.