A solution to one of Knuth's permutation problems

Details A solution to one of Knuth's permutation problems A solution to one of Knuth's permutation problems

2010-04-23

arxiv.org/abs/1004.4159v1

Mathematics

Combinatorics

4 pages, 2 figures.

Scientific paper

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.

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