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arXiv · 1004.4159

A solution to one of Knuth's permutation problems

Benjamin Young
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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.

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Benjamin Young. 2010-04-23. A solution to one of Knuth's permutation problems. https://arxiv.org/abs/1004.4159

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