Picture of athlete cycling

Open Access research with a real impact on health...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the Physical Activity for Health Group based within the School of Psychological Sciences & Health. Research here seeks to better understand how and why physical activity improves health, gain a better understanding of the amount, intensity, and type of physical activity needed for health benefits, and evaluate the effect of interventions to promote physical activity.

Explore open research content by Physical Activity for Health...

Involutions avoiding the class of permutations in Sk with prefix 12

Dukes, W. M. B. and Mansour, Toufik (2007) Involutions avoiding the class of permutations in Sk with prefix 12. In: 19th International Conference on Formal Power Series & Algebraic Combinatorics, 2007-07-02 - 2007-07-06, Nankai University.

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


An involution π is said to be τ-avoiding if it does not contain any subsequence having all the same pairwise comparisons as τ. This paper concerns the enumeration of involutions which avoid a set Ak of subsequences increasing both in number and in length at the same time. Let Ak be the set of all the permutations 12π3 . . . πk of length k. For k = 3 the only subsequence in Ak is 123 and the 123-avoiding involutions of length n are enumerated by the central binomial coefficients. For k = 4 we give a combinatorial explanation that shows the number of involutions of length n avoiding A4 is the same as the number of symmetric Schroder paths of length n − 1. For each k ≥ 3 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.