Alphabetic points in compositions and words

We use generating functions to account for alphabetic points (or the lack thereof) in compositions and words. An alphabetic point is a value $j$ such that all the values to its left are not larger than $j$ and all the values to its right are not smaller than $j$. We also provide the asymptotics for compositions and words which have no alphabetic points, as the size tends to infinity. This is achieved by the construction of upper and lower bounds which converge to each other, and in the latter case by probabilistic arguments. } \keywords{generating function, fixed point, derangement, composition, word, alphabetic points, strong fixed point, asymptotics