A solution to one of Knuth's permutation problems

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 W1 < W2 < ... < Wn, is dissected into n! pieces along the planes xi = xj. We describe which pieces have the same volume, and show that there are Cn distinct volumes, where Cn denotes the nth Catalan number.

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