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A Combinatorial proof of a result of Hetyei and Reiner on Foata-Strehl type permutation trees

Miklós Bóna
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Abstract

We give a combinatorial proof of the result of Hetyei and Reiner that there are exactly $n!/3$ permutations of length $n$ in the minmax tree representation of which the $i$th node is a leaf. We also prove the new result that the number of $n$-permutations in which this node has one child is $n!/3$ as well, implying that the same holds for those in which this node has two children.

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BibTeXRIS

Miklós Bóna. 1997-03-25. A Combinatorial proof of a result of Hetyei and Reiner on Foata-Strehl type permutation trees. https://arxiv.org/abs/math/9703209

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