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...

Enumeration of fixed points of an involution on β(1, 0)-trees

Kitaev, Sergey and de Mier, Anna (2014) Enumeration of fixed points of an involution on β(1, 0)-trees. Graphs and Combinatorics, 30 (5). pp. 1207-1221.

[img]
Preview
Text (Kitaev-de-Mier-GC2014-enumeration-of-fixed-points-of-an-involution)
Kitaev_de_Mier_GC2014_enumeration_of_fixed_points_of_an_involution.pdf - Accepted Author Manuscript

Download (354kB) | Preview

Abstract

β(1, 0)-trees provide a convenient description of rooted non-separable planar maps. The involution h on β(1, 0)-trees was introduced to prove a complicated equidistribution result on a class of pattern-avoiding permutations. In this paper, we describe and enumerate fixed points of the involution h. Intriguingly, the fixed points are equinumerous with the fixed points under taking the dual map on rooted non-separable planar maps, even though the fixed points do not go to each other under the know (natural) bijection between the trees and the maps.