Lyndon words, permutations and trees
✍ Scribed by Christophe Hohlweg; Christophe Reutenauer
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 197 KB
- Volume
- 307
- Category
- Article
- ISSN
- 0304-3975
No coin nor oath required. For personal study only.
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We define new Mahonian statistics, called MAD, MAK, and ENV, on words. Of these, ENV is shown to equal the classical INV, that is, the number of inversions, while for permutations MAK has been already defined by Foata and Zeilberger. It Ž . Ž . is shown that the triple statistics des, MAK, MAD and e
In this paper we exploit binary tree representations of permutations to give a combinatorial proof of Purtill's result [8] that where A n is the set of André permutations, v cd (σ ) is the cd-statistic of an André permutation and v ab (σ ) is the ab-statistic of a permutation. Using Purtill's proof