One may generalize integer compositions by replacing the positive integers with a different additive semigroup, giving the broader concept of a “composition over a semigroup”. Here we focus on semigroups which are finite groups and achieve asymptotic enumeration of compositions over a finite group which satisfy a local restriction. These compositions are associated to walks on a voltage graph whose structure is exploited to simplify asymptotic expressions. Specifically, we show that under mild conditions the number of locally restricted compositions of a group element is asymptotically independent of the particular group element. We apply this result to subword pattern avoidance and other examples such as generalized Carlitz compositions.

人们可以通过用不同的可加半群替换正整数来推广整数组合，从而给出“半群上的组合”的更广泛概念。在这里，我们关注作为有限群的半群，并在满足局部限制的有限群上实现组合的渐近枚举。这些组合与电压图上的游动相关联，该图的结构被用来简化渐近表达式。具体来说，我们表明，在温和条件下，族元素的局部受限组合的数量渐近独立于特定的族元素。我们将此结果应用于子词模式避免和其他示例，例如广义 Carlitz 组合。