ON NUMBER OF WAYS TO SHELL THE k-DIMENSIONAL TREES

Title & Authors
ON NUMBER OF WAYS TO SHELL THE k-DIMENSIONAL TREES
Chae, Gab-Byung; Cheong, Min-Seok; Kim, Sang-Mok;

Abstract
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 $\small{\frac{n!}{(k+1)!}(nk-k^2-k+1)!k}$.
Keywords
k-tree;recursive k-tree;shell;
Language
English
Cited by
References
1.
L. W. Beineke and R. E. Pippert, The number of labeled k-dimensional trees, J. Combinatorial Theory 6 (1969), 200-205

2.
G. Danaraj and V. Klee, Which spheres are shellable?, Ann. Discrete Math. 2 (1978), 33-52

3.
F. Harary, The number of linear, directed, rooted, and connected graphs, Trans. Amer. Math. Soc. 78 (1955), 445-463

4.
F. Harary and E. M. Palmer, On acyclic simplicial complexes, Mathematika 15 (1968), 115-122

5.
E. M. Palmer, On the number of labeled 2-trees, J. Combinatorial Theory 6 (1969), 206-207

6.
N. J. A. Sloane and S. Plouffe, The encyclopedia of integer sequences, With a separately available computer disk. Academic Press, Inc., San Diego, CA, 1995