Abstract
Purchase PDF (276 K)
E-mail Article
Add to my Quick Links
Cited By in Scopus (3)
Purchase PDF (390 K)
doi:10.1006/eujc.1998.0233 
Copyright © 1998 Academic Press. All rights reserved.
Regular Article
Permutation Trees and Variation Statistics*1
References and further reading may be available for this article. To view references and further reading you must purchase this article.
Received 25 June 1996;
Abstract
In this paper we exploit binary tree representations of permutations to give a combinatorial proof of Purtill's result [8] that
where
nis the set of André permutations,vcd(σ) is thecd-statistic of an André permutation andvab(σ) is theab-statistic of a permutation. Using Purtill's proof as a motivation we introduce a new ‘Foata–Strehl-like’ action on permutations. This
2n − 1-action allows us to give an elementary proof of Purtill's theorem, and a bijection between André permutations of the first kind and alternating permutations starting with a descent. A modified version of our group action leads to a new class of André-like permutations with structure similar to that of simsun permutations.
*1 The research of this author was supported by the UQAM Foundation.
f1 Current address: Mathematics Department, University of Kansas, Snow Hall, Lawrence KS, 66045, U.S.A. On leave from the Mathematical Institute of the Hungarian Academy of Sciences.
f2 Current address: INSERM U-436, Université Paris VI, 91, bd de l'Hôpital, 75013 Paris, France.
