Rationality, irrationality, and Wilf equivalence in generalized factor order

Sergey Kitaev, Jeffrey Liese, Jeffrey Remmel +1

Let $P$ be a partially ordered set and consider the free monoid $P^{\ast }$ of all words over $P$. If $w,w^{\prime }\in P^{\ast }$ then $w^{\prime }$ is a factor of $w$ if there are words $u,v$ with $w=u{w}^{\prime }v$. D…