Skip Navigation



The Computer Journal Advance Access published online on June 22, 2007
The Computer Journal, doi:10.1093/comjnl/bxm022
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
50/5/574    most recent
bxm022v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Juarna, A.
Right arrow Articles by Vajnovszki, V.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2007. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Some Generalizations Of a Simion–Schmidt Bijection

Asep Juarna and Vincent Vajnovszki*

LE2I—UMR CNRS, Université de Bourgogne, B.P. 47 870, 21078 Dijon Cedex, France

* Correspondence author: vvajnov{at}u-bourgogne.fr

Received 16 June 2006; revised 20 January 2007

In 1985, Simion and Schmidt gave a constructive bijection {varphi} from the set of all length (n – 1) binary strings having no two consecutive 1s to the set of all length n permutations avoiding all patterns in {123,132,213}. In this paper, we generalize {varphi} to an injective function from {0,1}n–1 to the set Sn of all length n permutations and derive from it four bijections {varphi} : P -> Q where P{subseteq}{0,1}n–1 and Q sub Sn. The domains are sets of restricted binary strings and the codomains are sets of pattern-avoiding permutations. As a particular case we retrieve the original Simion–Schmidt bijection. We also show that the bijections obtained are actually combinatorial isomorphisms, i.e. closeness-preserving bijections. Three of them have known Gray codes and generating algorithms for their domains and we present similar results for each corresponding codomain, under the appropriate combinatorial isomorphism.

Key Words: pattern-avoiding permutations • Fibonacci and Lucas strings • constructive bijections • combinatorial isomorphisms • Gray codes


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.