ON NUMBER OF WAYS TO SHELL THE k-DIMENSIONAL TREES
Gab-Byung Chae, Minseok Cheong, Sang‐Mok Kim · Bulletin of the Korean Mathematical Society · 2007
Which spheres are shellable?[2]. We present one of them which is the k-tree with n-labeled vertices. We found that the number of ways to shell the k-dimensional trees on n-labeled vertices is $$\frac{n!}{(k+1)!}(nk-k^2-k+1)!k$$ .