A solution to one of Knuth's permutation problems
Combinatorics
2010-04-26 v1
Abstract
We answer a problem posed recently by Knuth: an n-dimensional box, with edges lying on the positive coordinate axes and generic edge lengths W_1 < W_2 < ... < W_n, is dissected into n! pieces along the planes x_i = x_j. We describe which pieces have the same volume, and show that there are C_n distinct volumes, where C_n denotes the nth Catalan number.
Keywords
Cite
@article{arxiv.1004.4159,
title = {A solution to one of Knuth's permutation problems},
author = {Benjamin Young},
journal= {arXiv preprint arXiv:1004.4159},
year = {2010}
}
Comments
4 pages, 2 figures.