Skip Navigation



Bulletin of the London Mathematical Society Advance Access published online on September 22, 2009
Bulletin of the London Mathematical Society, doi:10.1112/blms/bdp071
This Article
Right arrow FREE Full Text (PDF) Freely available
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 Mansour, T.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2009 London Mathematical Society

Smooth partitions and Chebyshev polynomials

Toufik Mansour

Department of Mathematics
University of Haifa
31905 Haifa
Israel

Received 13 September 2008. Revision received 22 May 2009.

A partition of the set [n] = {1, 2, ..., n} is a collection {B1, ..., Bk} of nonempty disjoint subsets of [n] (called blocks) whose union equals [n]. A partition of [n] is said to be smooth if i isin Bs implies that i + 1 isin Bs–1 {cup} Bs {cup} Bs + 1 for all i isin [n–1] (B0 = Bk + 1 = {emptyset}). This paper presents the generating function for the number of k-block, smooth partitions of [n], written in terms of Chebyshev polynomials of the second kind. There follows a formula for the number of k-block, smooth partitions of [n] written in terms of trigonometric sums. Also, by first establishing a bijection between the set of smooth partitions of [n] and a class of symmetric Dyck paths of semilength 2n–1, we prove that the counting sequence for smooth partitions of [n] is Sloane's A005773.

2000 Mathematics Subject Classification 68R05, 05A05, 05A15, 05A16.


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.