A simple bijection between permutation matrices and descending plane partitions without special parts

Markus Fulmek

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arXiv · 1605.01227

A simple bijection between permutation matrices and descending plane partitions without special parts

Markus Fulmek

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Abstract

We present a simple bijection between permutation matrices and descending plane partitions without special parts. This bijection is already mentioned in work of P. Lalonde (without giving the details); it involves the inversion words of permutations and the (well-known) representation of descending plane partitions as families of non--intersecting lattice paths. (Taking a short detour, we will also exhibit how the (well--known) enumeration of descending plane partitions follows easily from the evaluation of Andrew's determinant.)

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Markus Fulmek. 2016-05-04. A simple bijection between permutation matrices and descending plane partitions without special parts. https://arxiv.org/abs/1605.01227

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