Number of Arrangements of Open Semicircles
Meng Zhao-jing · Journal of Hebei University · 2006
In an arrangement of n open semicircles on S~1,the weight of a vertex is defined to be the number of semicircles containing it.The number of vertices having weight k is denoted by v-k,v=(v-0,v-1,…,v-(n-1)) is called the v-vector of the arrangement.In this paper the number of different arrangements with a given v-vector is reckoned.