Picture of a black hole

Strathclyde Open Access research that creates ripples...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of research papers by University of Strathclyde researchers, including by Strathclyde physicists involved in observing gravitational waves and black hole mergers as part of the Laser Interferometer Gravitational-Wave Observatory (LIGO) - but also other internationally significant research from the Department of Physics. Discover why Strathclyde's physics research is making ripples...

Strathprints also exposes world leading research from the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

Discover more...

Symmetric Schröder paths and restricted involutions

Dukes, W.M.B. and Deng, Eva and Mansour, Toufik and Wu, Susan (2009) Symmetric Schröder paths and restricted involutions. Discrete Mathematics, 309 (12). pp. 4108-4115. ISSN 0012-365X

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

Let Ak be the set of permutations in the symmetric group Sk with prefix 12. This paper concerns the enumeration of involutions which avoid the set of patterns Ak. We present a bijection between symmetric Schroder paths of length $2n and involutions of length n+1 avoiding mathcalA4. Statistics such as the number of right-to-left maxima and fixed points of the involution correspond to the number of steps in the symmetric Schroder path of a particular type. For each k> 2 we determine the generating function for the number of involutions avoiding the subsequences in Ak, according to length, first entry and number of fixed points.