3 problems

Let $\mathbb{P}^*$ be the set of finite words over the positive integers, let $S(u;t,x)$ be the associated generating function, and let an increasing/decreasing factorization mean…

Let $\mathbb{P}^*$ be the set of finite words over the positive integers, let $\mathcal{F}(u)$ denote the set of words containing $u$ as a factor in generalized factor order, and l…

Let $P$ be the positive integers with their usual order, let $\mathbb{P}^*$ denote the set of finite words over $P$, and let $u\backsim v$ mean that the weight generating functions…